We investigate the long time existence of strong solutions to the initial value problem for the three-dimensional non-isentropic compressible Navier-Stokes-Korteweg system.Under the conditions of slight density and te...We investigate the long time existence of strong solutions to the initial value problem for the three-dimensional non-isentropic compressible Navier-Stokes-Korteweg system.Under the conditions of slight density and temperature variations,we verify that the full compressible Navier-Stokes-Korteweg equations admit a unique strong solution as long as the solution of the limiting system exists,when the Mach number is sufficiently small.Furthermore,we deduce the uniform convergence of strong solutions for the compressible system toward those for the corresponding incompressible system on the time interval in which the solution exists.展开更多
In this paper,a class of quaternion-valued cellular neural networks(QVCNNS)with time-varying delays are considered.Combining graph theory with the continuation theorem of Mawhin’s coincidence degree theory as well as...In this paper,a class of quaternion-valued cellular neural networks(QVCNNS)with time-varying delays are considered.Combining graph theory with the continuation theorem of Mawhin’s coincidence degree theory as well as Lyapunov functional method,we establish new criteria on the existence and exponential stability of periodic solutions for QVCNNS by removing the assumptions for the boundedness on the activation functions and the assumptions that the values of the activation functions are zero at origin.Hence,our results are less conservative and new.展开更多
We study the global existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker-Smale(for short,TCS) model coupled with Stokes equations in the whole space.The coupled system consists of the k...We study the global existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker-Smale(for short,TCS) model coupled with Stokes equations in the whole space.The coupled system consists of the kinetic TCS equation for a particle ensemble and the Stokes equations for a fluid via a drag force.In this paper,we present a complete analysis of the existence of global-in-time strong solutions to the coupled model without any smallness restrictions on the initial data.展开更多
This paper is concerned with the Cauchy problem for a 3D fluid-particle interaction model in the so-called flowing regime inℝ3.Under the smallness assumption on both the external potential and the initial perturbation...This paper is concerned with the Cauchy problem for a 3D fluid-particle interaction model in the so-called flowing regime inℝ3.Under the smallness assumption on both the external potential and the initial perturbation of the stationary solution in some Sobolev spaces,the existence and uniqueness of global smooth solutions in H3 of the system are established by using the careful energy method.展开更多
We study the existence of solutions for Kirchhoff-type equations.Firstly,we use the Sobolev inequality and the weakly lower semi-continuity of the norm to prove that the corresponding function can reach the global min...We study the existence of solutions for Kirchhoff-type equations.Firstly,we use the Sobolev inequality and the weakly lower semi-continuity of the norm to prove that the corresponding function can reach the global minimum.Then,we use the variational method and some analytical techniques to obtain the existence of the positive solution of the equation whenλis small enough.展开更多
We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.
In this study, we prove the of existence of solutions of a convolution Volterra integral equation in the space of the Lebesgue integrable function on the set of positive real numbers and with the standard norm defined...In this study, we prove the of existence of solutions of a convolution Volterra integral equation in the space of the Lebesgue integrable function on the set of positive real numbers and with the standard norm defined on it. An operator P was assigned to the convolution integral operator which was later expressed in terms of the superposition operator and the nonlinear operator. Given a ball B<sub>r</sub> belonging to the space L it was established that the operator P maps the ball into itself. The Hausdorff measure of noncompactness was then applied by first proving that given a set M∈ B r the set is bounded, closed, convex and nondecreasing. Finally, the Darbo fixed point theorem was applied on the measure obtained from the set E belonging to M. From this application, it was observed that the conditions for the Darbo fixed point theorem was satisfied. This indicated the presence of at least a fixed point for the integral equation which thereby implying the existence of solutions for the integral equation.展开更多
This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utiliz...This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utilizing cut-off techniques and combining with the Faedo Galerkin approximation method, local solvability was established. Based on the potential well method and Hardy Sobolev inequality, derive the global existence of the solution. In addition, we also obtained the results of decay.展开更多
This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones a...This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.展开更多
In this paper, we study the global existence of the smooth solution for a reduced quantum Zakharov system in two spatial dimensions. Using energy estimates and the logarithmic type Sobolev inequality, we show the glob...In this paper, we study the global existence of the smooth solution for a reduced quantum Zakharov system in two spatial dimensions. Using energy estimates and the logarithmic type Sobolev inequality, we show the global existence of the solution to this system without any small condition on the initial data.展开更多
国际原子能机构(IAEA)目前已经按2008年制定的长期结构(Long Term Structure)自上而下建立了由145项标准组成的安全标准体系,同时计划在2026年制定一个着眼于未来10~15年的新长期结构,以适应人工智能、气候变化、新型反应堆等带来的新...国际原子能机构(IAEA)目前已经按2008年制定的长期结构(Long Term Structure)自上而下建立了由145项标准组成的安全标准体系,同时计划在2026年制定一个着眼于未来10~15年的新长期结构,以适应人工智能、气候变化、新型反应堆等带来的新需求。本文介绍了IAEA辐射安全标准委员会(RASSC)的主要工作,并讨论了RASSC近期关注的辐射安全问题:针对现存照射辨识和管理方面的挑战,RASSC正在新制定一项关于现存照射的综合性安全导则;虽然国际放射防护委员会(ICRP)已经更新了职业人员内照射剂量系数,RASSC不会立即修订与之相关的安全标准,同时会持续关注成员国经验反馈;随着新型放疗技术的应用,RASSC近期还关注放射性核素治疗中的辐射防护、放疗患者的第二原发癌的风险。展开更多
针对建筑业转型升级及“新工科”建设的需求,如何升级土木类既有专业培养模式,并形成可持续的智能建造人才生态供给,已成为各高校面临的迫切任务。文章首先阐明了智能建造新专业建设与土木类既有专业升级之间的关联,借助OBE(Outcome Bas...针对建筑业转型升级及“新工科”建设的需求,如何升级土木类既有专业培养模式,并形成可持续的智能建造人才生态供给,已成为各高校面临的迫切任务。文章首先阐明了智能建造新专业建设与土木类既有专业升级之间的关联,借助OBE(Outcome Based Education)教育理念,提出了土木类既有专业升级改造面临的主要挑战,厘清了专业从局部课程到方案总体升级改造的基本思路。随后,以大连理工大学为例,探讨了土木类既有专业升级改造的具体途径。实践表明,明确培养目标、重构课程内容、优化知识结构、强化实践训练、提升教学能力、改进教学手段和创新管理机制是土木类既有专业升级改造的有效策略。该研究的结论可为其他高校土木类专业改革及教学研究提供参考。展开更多
文摘We investigate the long time existence of strong solutions to the initial value problem for the three-dimensional non-isentropic compressible Navier-Stokes-Korteweg system.Under the conditions of slight density and temperature variations,we verify that the full compressible Navier-Stokes-Korteweg equations admit a unique strong solution as long as the solution of the limiting system exists,when the Mach number is sufficiently small.Furthermore,we deduce the uniform convergence of strong solutions for the compressible system toward those for the corresponding incompressible system on the time interval in which the solution exists.
基金Supported by the Innovation Platform Open Fund in Hunan Province Colleges and Universities of China(201485).
文摘In this paper,a class of quaternion-valued cellular neural networks(QVCNNS)with time-varying delays are considered.Combining graph theory with the continuation theorem of Mawhin’s coincidence degree theory as well as Lyapunov functional method,we establish new criteria on the existence and exponential stability of periodic solutions for QVCNNS by removing the assumptions for the boundedness on the activation functions and the assumptions that the values of the activation functions are zero at origin.Hence,our results are less conservative and new.
基金supported by the National Natural Science Foundation of China (12001033)。
文摘We study the global existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker-Smale(for short,TCS) model coupled with Stokes equations in the whole space.The coupled system consists of the kinetic TCS equation for a particle ensemble and the Stokes equations for a fluid via a drag force.In this paper,we present a complete analysis of the existence of global-in-time strong solutions to the coupled model without any smallness restrictions on the initial data.
文摘This paper is concerned with the Cauchy problem for a 3D fluid-particle interaction model in the so-called flowing regime inℝ3.Under the smallness assumption on both the external potential and the initial perturbation of the stationary solution in some Sobolev spaces,the existence and uniqueness of global smooth solutions in H3 of the system are established by using the careful energy method.
文摘We study the existence of solutions for Kirchhoff-type equations.Firstly,we use the Sobolev inequality and the weakly lower semi-continuity of the norm to prove that the corresponding function can reach the global minimum.Then,we use the variational method and some analytical techniques to obtain the existence of the positive solution of the equation whenλis small enough.
文摘We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.
文摘In this study, we prove the of existence of solutions of a convolution Volterra integral equation in the space of the Lebesgue integrable function on the set of positive real numbers and with the standard norm defined on it. An operator P was assigned to the convolution integral operator which was later expressed in terms of the superposition operator and the nonlinear operator. Given a ball B<sub>r</sub> belonging to the space L it was established that the operator P maps the ball into itself. The Hausdorff measure of noncompactness was then applied by first proving that given a set M∈ B r the set is bounded, closed, convex and nondecreasing. Finally, the Darbo fixed point theorem was applied on the measure obtained from the set E belonging to M. From this application, it was observed that the conditions for the Darbo fixed point theorem was satisfied. This indicated the presence of at least a fixed point for the integral equation which thereby implying the existence of solutions for the integral equation.
文摘This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utilizing cut-off techniques and combining with the Faedo Galerkin approximation method, local solvability was established. Based on the potential well method and Hardy Sobolev inequality, derive the global existence of the solution. In addition, we also obtained the results of decay.
文摘This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.
文摘In this paper, we study the global existence of the smooth solution for a reduced quantum Zakharov system in two spatial dimensions. Using energy estimates and the logarithmic type Sobolev inequality, we show the global existence of the solution to this system without any small condition on the initial data.
文摘国际原子能机构(IAEA)目前已经按2008年制定的长期结构(Long Term Structure)自上而下建立了由145项标准组成的安全标准体系,同时计划在2026年制定一个着眼于未来10~15年的新长期结构,以适应人工智能、气候变化、新型反应堆等带来的新需求。本文介绍了IAEA辐射安全标准委员会(RASSC)的主要工作,并讨论了RASSC近期关注的辐射安全问题:针对现存照射辨识和管理方面的挑战,RASSC正在新制定一项关于现存照射的综合性安全导则;虽然国际放射防护委员会(ICRP)已经更新了职业人员内照射剂量系数,RASSC不会立即修订与之相关的安全标准,同时会持续关注成员国经验反馈;随着新型放疗技术的应用,RASSC近期还关注放射性核素治疗中的辐射防护、放疗患者的第二原发癌的风险。
文摘针对建筑业转型升级及“新工科”建设的需求,如何升级土木类既有专业培养模式,并形成可持续的智能建造人才生态供给,已成为各高校面临的迫切任务。文章首先阐明了智能建造新专业建设与土木类既有专业升级之间的关联,借助OBE(Outcome Based Education)教育理念,提出了土木类既有专业升级改造面临的主要挑战,厘清了专业从局部课程到方案总体升级改造的基本思路。随后,以大连理工大学为例,探讨了土木类既有专业升级改造的具体途径。实践表明,明确培养目标、重构课程内容、优化知识结构、强化实践训练、提升教学能力、改进教学手段和创新管理机制是土木类既有专业升级改造的有效策略。该研究的结论可为其他高校土木类专业改革及教学研究提供参考。
