As China in the decades ahead is to go through significant reorganization in the power sector and the petrochemical industry will see considerable growth,the transportation infrastructure for petroleum and gas should ...As China in the decades ahead is to go through significant reorganization in the power sector and the petrochemical industry will see considerable growth,the transportation infrastructure for petroleum and gas should have a new shape. Implementing the largest infrastructure projects and creating on this basis a modern transportation network will not only see a new reincarnation of traditional industrial centers, but also open wider opportunities for regional development.展开更多
At present,suicide behaviors of college students frequently occur in colleges,but the problem of why college students suicide has always plagued many college educators.From the perspective of Levinas’view of existenc...At present,suicide behaviors of college students frequently occur in colleges,but the problem of why college students suicide has always plagued many college educators.From the perspective of Levinas’view of existence,suicide is the last control that people can have over existence.Suicide includes a person’s three mental states:exhaustion,laziness,and boredom,and it can orderly induce three standpoints of death:“I have to die”,“I want to die”,and“I am going to die”.Knowing the problems of suicide is helpful to help college educators better understand the suicidal behavior of college students and help them better carry out the life education of college students.展开更多
The deformation caused by tunnel excavation is quite important for safety,especially when it is adjacent to the existing tunnel.Nevertheless,the investigation of deformation characteristics in overlapped curved shield...The deformation caused by tunnel excavation is quite important for safety,especially when it is adjacent to the existing tunnel.Nevertheless,the investigation of deformation characteristics in overlapped curved shield tunneling remains inadequate.The analytical solution for calculating the deformation of the ground and existing tunnel induced by overlapped curved shield tunneling is derived by the Mirror theory,Mindlin solution and Euler-Bernoulli-Pasternak model,subsequently validated through both finite element simulation and field monitoring.It is determined that the overcutting plays a crucial role in the ground settlement resulting from curved shield tunneling compared to straight shield tunneling.The longitudinal settlement distribution can be categorized into five areas,with the area near the tunnel surface experiencing the most dramatic settlement changes.The deformation of the existing tunnel varies most significantly with turning radius compared to tunnel clearance and grouting pressure,especially when the turning radius is less than 30 times the tunnel diameter.The tunnel crown exhibits larger displacement than the tunnel bottom,resulting in a distinctive‘vertical egg'shape.Furthermore,an optimized overcutting mode is proposed,involving precise control of the extension speed and angular velocity of the overcutting cutter,which effectively mitigates ground deformation,ensuring the protection of the existing tunnel during the construction.展开更多
This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreov...This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreover,we establish the controllability of the considered system.To do so,first,we investigate the approximate controllability of the corresponding linear system.Subsequently,we prove the nonlinear system is approximately controllable if the corresponding linear system is approximately controllable.To reach the conclusions,the theory of resolvent operators,the Banach contraction mapping principle,and fixed point theorems are used.While concluding,some examples are given to demonstrate the efficacy of the proposed results.展开更多
This paper mainly studies the well-posedness of steady incompressible impinging jet flow problem through a 3D axisymmetric finitely long nozzle.This problem originates from the physical phenomena encountered in practi...This paper mainly studies the well-posedness of steady incompressible impinging jet flow problem through a 3D axisymmetric finitely long nozzle.This problem originates from the physical phenomena encountered in practical engineering fields,such as in short take-off and vertical landing(STOVL)aircraft.Nowadays many intricate phenomena associated with impinging jet flows remain inadequately elucidated,which limits the ability to optimize aircraft design.Given a boundary condition in the inlet,the impinging jet problem is transformed into a Bernoulli-type free boundary problem according to the stream function.Then the variational method is used to study the corresponding variational problem with one parameter,thereby the wellposedness is established.The main conclusion is as follows.For a 3D axisymmetric finitely long nozzle and an infinitely long vertical wall,given an axial velocity in the inlet of nozzle,there exists a unique smooth incom‑pressible impinging jet flow such that the free boundary initiates smoothly at the endpoint of the nozzle and extends to infinity along the vertical wall at far fields.The key point is to investigate the regularity of the corner where the nozzle and the vertical axis intersect.展开更多
In this work,we re-investigate a classical mathematical model of untreated HIV infection suggested by Kirschner and introduce a novel non-standard finite-difference method for its numerical solution.As our first contr...In this work,we re-investigate a classical mathematical model of untreated HIV infection suggested by Kirschner and introduce a novel non-standard finite-difference method for its numerical solution.As our first contribution,we establish non-negativity,boundedness of some solution components,existence globally in time,and uniqueness on a time interval[0,T]for an arbitrary T>0 for the time-continuous problem which extends known results of Kirschner’s model in the literature.As our second analytical result,we establish different equilibrium states and examine their stability properties in the time-continuous setting or discuss some numerical tools to evaluate this question.Our third contribution is the formulation of a non-standard finite-difference method which preserves non-negativity,boundedness of some time-discrete solution components,equilibria,and their stabilities.As our final theoretical result,we prove linear convergence of our non-standard finite-difference-formulation towards the time-continuous solution.Conclusively,we present numerical examples to illustrate our theoretical findings.展开更多
Objective:To explore symptom experiences and self-coping patterns during the early and late stages of chemotherapy in these patients to provide a basis for developing targeted symptom management strategies.Methods:A t...Objective:To explore symptom experiences and self-coping patterns during the early and late stages of chemotherapy in these patients to provide a basis for developing targeted symptom management strategies.Methods:A total of 27 patients with pancreatic cancer undergoing chemotherapy at two medical institutions were recruited between November 2023 and August 2024.Semi-structured interviews were conducted in person or over the phone.Data were analyzed using traditional content and thematic analyses.Results:Three themes were identified:symptom experience,self-coping patterns,and existing obstacles.During the early stages of chemotherapy,patients reported a higher frequency of unpleasant symptoms and recognized these symptoms earlier in the treatment course.Patients in the early stages primarily relied on external support to cope with symptoms,while those in the later stages adopted self-care strategies.Several challenges related to unpleasant symptoms were observed,which appeared to correlate with the self-coping patterns employed.Conclusion:Patients with pancreatic cancer undergoing chemotherapy experience a complex and diverse range of symptoms,with varying coping patterns at different stages of treatment.Symptom management during chemotherapy presents significant challenges.Healthcare providers should improve the ongoing monitoring of symptoms post-chemotherapy.By linking patients’symptom experiences and self-coping patterns at different stages of chemotherapy to their specific challenges,personalized symptom management strategies can be developed to enhance care quality.展开更多
This paper proposes a mixed game with finitely many leaders and follower populations.In such a game,two types of equilibria are defined.First,a Nash equilibrium is introduced for the scenario in which leaders and foll...This paper proposes a mixed game with finitely many leaders and follower populations.In such a game,two types of equilibria are defined.First,a Nash equilibrium is introduced for the scenario in which leaders and follower populations are in perfect competition,each maximizing its own payoff.Second,a cooperative equilibrium is proposed for the case where leaders and follower populations,respectively,form coalitions and cooperate.Moreover,the existence of both Nash and cooperative equilibria is proved under the condition that the payoff functions are continuous and quasi-concave.Finally,we demonstrate the generic stability of cooperative equilibria in mixed games.More concretely,in the sense of Baire category,the cooperative equilibria in most mixed games are stable under perturbations of the payoff functions.In short,this paper presents two main contributions.On the one hand,we provide a novel mixed-game framework,which differs from both classical leader-follower games and leader-follower population games.On the other hand,the Nash and cooperative equilibria in our mixed games are distinct from those in existing leader-follower population games.The results are further illustrated with examples.展开更多
In this paper,we study the weighted higher order semilinear equation in an exterior domain(-△)^(m)u=|x|^(α)g(u)in R^(N)\B_(R_(0)),where N≥1,m≥2 are integers,α>-2m,g is a continuous and nondecreasing function i...In this paper,we study the weighted higher order semilinear equation in an exterior domain(-△)^(m)u=|x|^(α)g(u)in R^(N)\B_(R_(0)),where N≥1,m≥2 are integers,α>-2m,g is a continuous and nondecreasing function in(0,+∞)and positive in(0,+∞),B_(R_(0))is the ball of the radius R0 centered at the origin.We prove that a positive supersolution of the problem which verifies(-△)_(i)u>0 in R^(N)\B_(R_(0))(i=0,…,m-1)exists if and only if N>2m and∫_(0)^(δ)g(t)/t^(2(N-m)+α/N-2m)dt<∞,,for someδ>0.We further obtain some existence and nonexistence results for the positive solution to the Dirichlet problem when g(u)=u^(p)with p>1,by using the Pohozaev identity and an embedding lemma of radial Sobolev spaces.展开更多
In this manuscript,a class of multi-term delay fractional differential equations(FDEs)under the Hilfer derivative is considered.Some newly updated results are established under boundary conditions.For the required res...In this manuscript,a class of multi-term delay fractional differential equations(FDEs)under the Hilfer derivative is considered.Some newly updated results are established under boundary conditions.For the required results,we utilize the fixed point theory and tools of the nonlinear functional analysis.Further keeping in mind the importance of stability results,we develop some adequate results about the said aspect.The Hyers-Ulam(H-U)-type concept is used to derive the required stability for the solution of the considered problem.Finally,by appropriate test problems,we justify our findings.展开更多
The construction of the new tunnel under the existing railway will break the original stress balance in the engineering area, resulting in the secondary redistribution of surrounding rock stress. The large amount of e...The construction of the new tunnel under the existing railway will break the original stress balance in the engineering area, resulting in the secondary redistribution of surrounding rock stress. The large amount of excavation unloading of the soil below is also easy to induce the uneven settlement deformation of the existing structure above, affecting the safety of driving. Based on the shield tunnel project between Caoqiao Station and Lize Business District Station of Beijing Metro, this paper restores the construction site by constructing the finite element numerical model of the project area, calculates and analyzes the deformation and stress of the existing railway structure before and after the construction of the tunnel, and determines the safety impact of the new structure on the existing railway. The results show that the shield tunnel undercrossing construction will cause the “concave” settlement of the railway subgrade above. Under the condition of grouting reinforcement, the “concave” settlement curve is slower and the distribution range is wider. With the advancement of the construction step, the settlement deformation of the subgrade gradually increases. When the tunnel approaches and passes directly below the subgrade, the settlement deformation curve of the subgrade changes from slow to steep. After the tunnel passes away, the curve changes from steep to slow, and the deformation of the subgrade reaches the maximum after the tunnel is connected. Under the grouting condition, the maximum settlement deformation of the subgrade is 2.08 mm, which is about 45% of the settlement deformation of the subgrade under the non-grouting condition. The ground grouting reinforcement can effectively control the subgrade settlement, and the field monitoring verifies the rationality of the calculation results. After the tunnel passes underneath, the most unfavorable section of the existing railway frame bridge is located at the top plate of the structure, and the maximum crack width is 0.178 mm. After grouting reinforcement, the stress environment of the structure is improved, the crack width generated by the structure is smaller, the reinforcement area required for calculation is less, and the structural safety meets the requirements.展开更多
As an integral part of China’s higher education system,higher vocational colleges play a significant role in talent cultivation,social services,and cultural inheritance.With the development of the times and the advan...As an integral part of China’s higher education system,higher vocational colleges play a significant role in talent cultivation,social services,and cultural inheritance.With the development of the times and the advancement of educational reform,the role of scientific research in higher vocational colleges has become increasingly prominent.This paper started from the necessity of conducting scientific research in higher vocational colleges,providing an in-depth analysis of its importance in improving teaching quality,promoting teachers’professional development,driving social services,and enhancing the college’s core competitiveness.At the same time,addressing the existing problems in current scientific research work at higher vocational colleges,this paper proposed innovative pathways focusing on the scientific research management system,scientific research team construction,scientific research funding investment,and scientific research outcome transformation.The aim is to provide valuable references for the scientific research development of higher vocational colleges.展开更多
In this paper,we prove an existence and uniqueness theorem of the solution for strongly pseudomonotone variational inequalities in reflexive Banach spaces.Based on this result,and investigate the stability behavior of...In this paper,we prove an existence and uniqueness theorem of the solution for strongly pseudomonotone variational inequalities in reflexive Banach spaces.Based on this result,and investigate the stability behavior of the perturbed variational inequalities.Moreover,we obtain an existence theorem of solutions for strongly quasimonotone variational inequalities in finite dimensional spaces.展开更多
In this paper,we consider an initial boundary value problem for the nonhomo-geneous heat-conducting magnetohydrodynamic fuids when the viscosityμ,magnetic dif-fusivity v and heat conductivity k depend on the temperat...In this paper,we consider an initial boundary value problem for the nonhomo-geneous heat-conducting magnetohydrodynamic fuids when the viscosityμ,magnetic dif-fusivity v and heat conductivity k depend on the temperature according to μ(0)=°,k(0)=08,v(0)=07,withα,>0,β≥0.We prove the global existence of a unique strong solution provided that ■ is suitably small.In addition,we also get some results of the large-time behavior and exponential decay estimates.展开更多
We consider the Cauchy problem for the three-dimensional pressureless Navier-Stokes/Navier-Stokes system,which consists of the pressureless Navier-Stokes equations for(n,w)coupled with the isentropic compressible Navi...We consider the Cauchy problem for the three-dimensional pressureless Navier-Stokes/Navier-Stokes system,which consists of the pressureless Navier-Stokes equations for(n,w)coupled with the isentropic compressible Navier-Stokes equations for(ρ,u)through a drag force term n(w−u).We prove the global existence of strong solutions to the coupled system when the initial data are small perturbations of the constant equilibrium state.However,due to the pressureless structure,one can only deal with the density n of the pressureless flow through the transport equation and it is crucial to obtain the exact time-decay rates for the corresponding velocity w of the pressureless flow.To this end,we make use of the spectral analysis,low-high frequency decomposition and time-weighted energy method to deduce the large time behavior of(w,ρ,u)and consequently establish the Lyapunov stability of the density n in Sobolev space.展开更多
文摘As China in the decades ahead is to go through significant reorganization in the power sector and the petrochemical industry will see considerable growth,the transportation infrastructure for petroleum and gas should have a new shape. Implementing the largest infrastructure projects and creating on this basis a modern transportation network will not only see a new reincarnation of traditional industrial centers, but also open wider opportunities for regional development.
文摘At present,suicide behaviors of college students frequently occur in colleges,but the problem of why college students suicide has always plagued many college educators.From the perspective of Levinas’view of existence,suicide is the last control that people can have over existence.Suicide includes a person’s three mental states:exhaustion,laziness,and boredom,and it can orderly induce three standpoints of death:“I have to die”,“I want to die”,and“I am going to die”.Knowing the problems of suicide is helpful to help college educators better understand the suicidal behavior of college students and help them better carry out the life education of college students.
基金financially supported by the National Natural Science Foundation of China(Grant No.52078334)the National Key Research and Development Program of China(Grant No.2017YFC0805402)the Tianjin Research Innovation Project for Postgraduate Students(Grant No.2021YJSB141).
文摘The deformation caused by tunnel excavation is quite important for safety,especially when it is adjacent to the existing tunnel.Nevertheless,the investigation of deformation characteristics in overlapped curved shield tunneling remains inadequate.The analytical solution for calculating the deformation of the ground and existing tunnel induced by overlapped curved shield tunneling is derived by the Mirror theory,Mindlin solution and Euler-Bernoulli-Pasternak model,subsequently validated through both finite element simulation and field monitoring.It is determined that the overcutting plays a crucial role in the ground settlement resulting from curved shield tunneling compared to straight shield tunneling.The longitudinal settlement distribution can be categorized into five areas,with the area near the tunnel surface experiencing the most dramatic settlement changes.The deformation of the existing tunnel varies most significantly with turning radius compared to tunnel clearance and grouting pressure,especially when the turning radius is less than 30 times the tunnel diameter.The tunnel crown exhibits larger displacement than the tunnel bottom,resulting in a distinctive‘vertical egg'shape.Furthermore,an optimized overcutting mode is proposed,involving precise control of the extension speed and angular velocity of the overcutting cutter,which effectively mitigates ground deformation,ensuring the protection of the existing tunnel during the construction.
文摘This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreover,we establish the controllability of the considered system.To do so,first,we investigate the approximate controllability of the corresponding linear system.Subsequently,we prove the nonlinear system is approximately controllable if the corresponding linear system is approximately controllable.To reach the conclusions,the theory of resolvent operators,the Banach contraction mapping principle,and fixed point theorems are used.While concluding,some examples are given to demonstrate the efficacy of the proposed results.
文摘This paper mainly studies the well-posedness of steady incompressible impinging jet flow problem through a 3D axisymmetric finitely long nozzle.This problem originates from the physical phenomena encountered in practical engineering fields,such as in short take-off and vertical landing(STOVL)aircraft.Nowadays many intricate phenomena associated with impinging jet flows remain inadequately elucidated,which limits the ability to optimize aircraft design.Given a boundary condition in the inlet,the impinging jet problem is transformed into a Bernoulli-type free boundary problem according to the stream function.Then the variational method is used to study the corresponding variational problem with one parameter,thereby the wellposedness is established.The main conclusion is as follows.For a 3D axisymmetric finitely long nozzle and an infinitely long vertical wall,given an axial velocity in the inlet of nozzle,there exists a unique smooth incom‑pressible impinging jet flow such that the free boundary initiates smoothly at the endpoint of the nozzle and extends to infinity along the vertical wall at far fields.The key point is to investigate the regularity of the corner where the nozzle and the vertical axis intersect.
文摘In this work,we re-investigate a classical mathematical model of untreated HIV infection suggested by Kirschner and introduce a novel non-standard finite-difference method for its numerical solution.As our first contribution,we establish non-negativity,boundedness of some solution components,existence globally in time,and uniqueness on a time interval[0,T]for an arbitrary T>0 for the time-continuous problem which extends known results of Kirschner’s model in the literature.As our second analytical result,we establish different equilibrium states and examine their stability properties in the time-continuous setting or discuss some numerical tools to evaluate this question.Our third contribution is the formulation of a non-standard finite-difference method which preserves non-negativity,boundedness of some time-discrete solution components,equilibria,and their stabilities.As our final theoretical result,we prove linear convergence of our non-standard finite-difference-formulation towards the time-continuous solution.Conclusively,we present numerical examples to illustrate our theoretical findings.
基金supported by the State Key Laboratory of Ultrasonic Medical Engineering/the Chongqing Science and Technology Bureau(Project No.2022KFKT7011)the Postdoctoral Fellowship Program of CPSF(GZC20233357)+1 种基金the Health Commission of Sichuan Province Medical Science and Technology Program(24QNMP007)the Medical Research Program of Health Commission of Chengdu(2023535).
文摘Objective:To explore symptom experiences and self-coping patterns during the early and late stages of chemotherapy in these patients to provide a basis for developing targeted symptom management strategies.Methods:A total of 27 patients with pancreatic cancer undergoing chemotherapy at two medical institutions were recruited between November 2023 and August 2024.Semi-structured interviews were conducted in person or over the phone.Data were analyzed using traditional content and thematic analyses.Results:Three themes were identified:symptom experience,self-coping patterns,and existing obstacles.During the early stages of chemotherapy,patients reported a higher frequency of unpleasant symptoms and recognized these symptoms earlier in the treatment course.Patients in the early stages primarily relied on external support to cope with symptoms,while those in the later stages adopted self-care strategies.Several challenges related to unpleasant symptoms were observed,which appeared to correlate with the self-coping patterns employed.Conclusion:Patients with pancreatic cancer undergoing chemotherapy experience a complex and diverse range of symptoms,with varying coping patterns at different stages of treatment.Symptom management during chemotherapy presents significant challenges.Healthcare providers should improve the ongoing monitoring of symptoms post-chemotherapy.By linking patients’symptom experiences and self-coping patterns at different stages of chemotherapy to their specific challenges,personalized symptom management strategies can be developed to enhance care quality.
基金supported by the National Natural Science Foundation of China(Grant No.11271098)the Guizhou Provincial Basic Research Program(Grant No.MS[2025]676)。
文摘This paper proposes a mixed game with finitely many leaders and follower populations.In such a game,two types of equilibria are defined.First,a Nash equilibrium is introduced for the scenario in which leaders and follower populations are in perfect competition,each maximizing its own payoff.Second,a cooperative equilibrium is proposed for the case where leaders and follower populations,respectively,form coalitions and cooperate.Moreover,the existence of both Nash and cooperative equilibria is proved under the condition that the payoff functions are continuous and quasi-concave.Finally,we demonstrate the generic stability of cooperative equilibria in mixed games.More concretely,in the sense of Baire category,the cooperative equilibria in most mixed games are stable under perturbations of the payoff functions.In short,this paper presents two main contributions.On the one hand,we provide a novel mixed-game framework,which differs from both classical leader-follower games and leader-follower population games.On the other hand,the Nash and cooperative equilibria in our mixed games are distinct from those in existing leader-follower population games.The results are further illustrated with examples.
文摘In this paper,we study the weighted higher order semilinear equation in an exterior domain(-△)^(m)u=|x|^(α)g(u)in R^(N)\B_(R_(0)),where N≥1,m≥2 are integers,α>-2m,g is a continuous and nondecreasing function in(0,+∞)and positive in(0,+∞),B_(R_(0))is the ball of the radius R0 centered at the origin.We prove that a positive supersolution of the problem which verifies(-△)_(i)u>0 in R^(N)\B_(R_(0))(i=0,…,m-1)exists if and only if N>2m and∫_(0)^(δ)g(t)/t^(2(N-m)+α/N-2m)dt<∞,,for someδ>0.We further obtain some existence and nonexistence results for the positive solution to the Dirichlet problem when g(u)=u^(p)with p>1,by using the Pohozaev identity and an embedding lemma of radial Sobolev spaces.
文摘In this manuscript,a class of multi-term delay fractional differential equations(FDEs)under the Hilfer derivative is considered.Some newly updated results are established under boundary conditions.For the required results,we utilize the fixed point theory and tools of the nonlinear functional analysis.Further keeping in mind the importance of stability results,we develop some adequate results about the said aspect.The Hyers-Ulam(H-U)-type concept is used to derive the required stability for the solution of the considered problem.Finally,by appropriate test problems,we justify our findings.
文摘The construction of the new tunnel under the existing railway will break the original stress balance in the engineering area, resulting in the secondary redistribution of surrounding rock stress. The large amount of excavation unloading of the soil below is also easy to induce the uneven settlement deformation of the existing structure above, affecting the safety of driving. Based on the shield tunnel project between Caoqiao Station and Lize Business District Station of Beijing Metro, this paper restores the construction site by constructing the finite element numerical model of the project area, calculates and analyzes the deformation and stress of the existing railway structure before and after the construction of the tunnel, and determines the safety impact of the new structure on the existing railway. The results show that the shield tunnel undercrossing construction will cause the “concave” settlement of the railway subgrade above. Under the condition of grouting reinforcement, the “concave” settlement curve is slower and the distribution range is wider. With the advancement of the construction step, the settlement deformation of the subgrade gradually increases. When the tunnel approaches and passes directly below the subgrade, the settlement deformation curve of the subgrade changes from slow to steep. After the tunnel passes away, the curve changes from steep to slow, and the deformation of the subgrade reaches the maximum after the tunnel is connected. Under the grouting condition, the maximum settlement deformation of the subgrade is 2.08 mm, which is about 45% of the settlement deformation of the subgrade under the non-grouting condition. The ground grouting reinforcement can effectively control the subgrade settlement, and the field monitoring verifies the rationality of the calculation results. After the tunnel passes underneath, the most unfavorable section of the existing railway frame bridge is located at the top plate of the structure, and the maximum crack width is 0.178 mm. After grouting reinforcement, the stress environment of the structure is improved, the crack width generated by the structure is smaller, the reinforcement area required for calculation is less, and the structural safety meets the requirements.
文摘As an integral part of China’s higher education system,higher vocational colleges play a significant role in talent cultivation,social services,and cultural inheritance.With the development of the times and the advancement of educational reform,the role of scientific research in higher vocational colleges has become increasingly prominent.This paper started from the necessity of conducting scientific research in higher vocational colleges,providing an in-depth analysis of its importance in improving teaching quality,promoting teachers’professional development,driving social services,and enhancing the college’s core competitiveness.At the same time,addressing the existing problems in current scientific research work at higher vocational colleges,this paper proposed innovative pathways focusing on the scientific research management system,scientific research team construction,scientific research funding investment,and scientific research outcome transformation.The aim is to provide valuable references for the scientific research development of higher vocational colleges.
文摘In this paper,we prove an existence and uniqueness theorem of the solution for strongly pseudomonotone variational inequalities in reflexive Banach spaces.Based on this result,and investigate the stability behavior of the perturbed variational inequalities.Moreover,we obtain an existence theorem of solutions for strongly quasimonotone variational inequalities in finite dimensional spaces.
基金supported by the National Natural Science Foundation of China(No.11931013)the Natural Science Foundation of Guangxi Province(No.2022GXNSFDA035078)the Foundamental Research Funds for the Central Universities,CHD(No.300102122115).
文摘In this paper,we consider an initial boundary value problem for the nonhomo-geneous heat-conducting magnetohydrodynamic fuids when the viscosityμ,magnetic dif-fusivity v and heat conductivity k depend on the temperature according to μ(0)=°,k(0)=08,v(0)=07,withα,>0,β≥0.We prove the global existence of a unique strong solution provided that ■ is suitably small.In addition,we also get some results of the large-time behavior and exponential decay estimates.
基金supported by the National Natural Science Foundation of China(11931010,12226326,12226327)the Key Research Project of Academy for Multidisciplinary Studies,Capital Normal Universitysupported by the Anhui Provincial Natural Science Foundation(2408085QA031).
文摘We consider the Cauchy problem for the three-dimensional pressureless Navier-Stokes/Navier-Stokes system,which consists of the pressureless Navier-Stokes equations for(n,w)coupled with the isentropic compressible Navier-Stokes equations for(ρ,u)through a drag force term n(w−u).We prove the global existence of strong solutions to the coupled system when the initial data are small perturbations of the constant equilibrium state.However,due to the pressureless structure,one can only deal with the density n of the pressureless flow through the transport equation and it is crucial to obtain the exact time-decay rates for the corresponding velocity w of the pressureless flow.To this end,we make use of the spectral analysis,low-high frequency decomposition and time-weighted energy method to deduce the large time behavior of(w,ρ,u)and consequently establish the Lyapunov stability of the density n in Sobolev space.
