In this paper,we prove the local existence and uniqueness of solutions to the evolutionary model for magnetoviscoelasticity in R^(2),R^(3).This model consists of an incompressible Navier-Stokes,a regularized system fo...In this paper,we prove the local existence and uniqueness of solutions to the evolutionary model for magnetoviscoelasticity in R^(2),R^(3).This model consists of an incompressible Navier-Stokes,a regularized system for the evolution of the deformation gradient and the Landau-Lifshitz-Gilbert system for the dynamics of the mag-netization.Our approach depends on approximating the system with a sequence of perturbed systems.展开更多
The regularity of the Cauchy problem for a generalized Camassa-Holm type equation is investigated. The pseudoparabolic regularization approach is employed to obtain some prior estimates under certain assumptions on th...The regularity of the Cauchy problem for a generalized Camassa-Holm type equation is investigated. The pseudoparabolic regularization approach is employed to obtain some prior estimates under certain assumptions on the initial value of the equation. The local existence of its solution in Sobolev space Hs （R） with 1 〈 s ≤ 3/2 is derived.展开更多
In this paper,we study the existence of localized nodal solutions for Schrodinger-Poisson systems with critical growth{−ε^(2)Δv+V(x)v+λψv=v^(5)+μ|v|^(q−2)v,in R^(3),−ε^(2)Δψ=v^(2),in R^(3);v(x)→0,ψ(x)→0as|x...In this paper,we study the existence of localized nodal solutions for Schrodinger-Poisson systems with critical growth{−ε^(2)Δv+V(x)v+λψv=v^(5)+μ|v|^(q−2)v,in R^(3),−ε^(2)Δψ=v^(2),in R^(3);v(x)→0,ψ(x)→0as|x|→∞.We establish,for smallε,the existence of a sequence of localized nodal solutions concentrating near a given local minimum point of the potential function via the perturbation method,and employ some new analytical skills to overcome the obstacles caused by the nonlocal term φu(x)=1/4π∫R^(3)u^(2)(y)/|x−y|dy.Our results improve and extend related ones in the literature.展开更多
We study the local analytic solutions f of the functional equation f（ψ（zf（z））） = φ（f（z）） for z in some neighborhood of the origin. Whether the solution f vanishes at z = 0 or not plays a critical role for ...We study the local analytic solutions f of the functional equation f（ψ（zf（z））） = φ（f（z）） for z in some neighborhood of the origin. Whether the solution f vanishes at z = 0 or not plays a critical role for local analytic solutions of this equation. In this paper, we obtain results of analytic solutions not only in the case f（0） = 0 but also for f（0） ≠ 0. When assuming f（0） = 0, for technical reasons, we just get the result for f′（0）≠ 0. Then when assuming f（0） = ω0 ≠ 0, ψ（0） = s # 0, ψ（z） is analytic at z = 0 and ψ（z） is analytic at z = ω0, we give the existence of local analytic solutions f in the case of 0 〈 ｜sω0｜ 〈 1 and the case of ｜sω0｜ = 1 with the Brjuno condition.展开更多
A localized space-time method of fundamental solutions(LSTMFS)is extended for solving three-dimensional transient diffusion problems in this paper.The interval segmentation in temporal direction is developed for the a...A localized space-time method of fundamental solutions(LSTMFS)is extended for solving three-dimensional transient diffusion problems in this paper.The interval segmentation in temporal direction is developed for the accurate simulation of long-time-dependent diffusion problems.In the LSTMFS,the whole space-time domain with nodes arranged i divided into a series of overlapping subdomains with a simple geometry.In each subdomain,the conventional method of fundamental solutions is utilized and the coefficients associated with the considered domain can be explicitly determined.By calculating a combined sparse matrix system,the value at any node inside the space-time domain can be obtained.Numerical experi-ments demonstrate that high accuracy and efficiency can be simultaneously achieved via the LSTMFS,even for the problems defined on a long-time and quite complex computational domain.展开更多
With the straification theory we have proved the transversal layer s 0 3,k (D) of complete equations for mixed fluid is not an empty set: s 0 3,k (D) ≠ for all k(k≥1) . Based on this conclusion a...With the straification theory we have proved the transversal layer s 0 3,k (D) of complete equations for mixed fluid is not an empty set: s 0 3,k (D) ≠ for all k(k≥1) . Based on this conclusion and the “secondary equation” of s 0 3,k (D), this paper fully presents the expressions of coefficients in all local analytic solutions of the equations. Therefore we provide the calculation formulas by which we can get the numerical solutions to any desired accuracy.展开更多
By means of the modified Clarkson and Kruskal （CK） direct method and the variable separation approach, we investigate the （24-1）-dimensional Ito equation which was constructed by Ito in 1980. The full symmetry gro...By means of the modified Clarkson and Kruskal （CK） direct method and the variable separation approach, we investigate the （24-1）-dimensional Ito equation which was constructed by Ito in 1980. The full symmetry group with the Kac-Moody-Virasoro algebra structure and the variable separation solutions are obtained. By selecting appropriate arbitrary functions, some special soliton excitations are shown graphically. The results presented here would be beneficial for understanding the （2-t-1）-dimensional Ito equation better.展开更多
Based on a special transformation that we introduce,the N-soliton solution of the(2+1)-dimensional Boiti–Leon–Manna–Pempinelli equation is constructed.By applying the long wave limit and restricting certain conjuga...Based on a special transformation that we introduce,the N-soliton solution of the(2+1)-dimensional Boiti–Leon–Manna–Pempinelli equation is constructed.By applying the long wave limit and restricting certain conjugation conditions to the related solitons,some novel localized wave solutions are obtained,which contain higher-order breathers and lumps as well as their interactions.In particular,by choosing appropriate parameters involved in the N-solitons,two interaction solutions mixed by a bell-shaped soliton and one breather or by a bell-shaped soliton and one lump are constructed from the 3-soliton solution.Five solutions including two breathers,two lumps,and interaction solutions between one breather and two bell-shaped solitons,one breather and one lump,or one lump and two bell-shaped solitons are constructed from the4-soliton solution.Five interaction solutions mixed by one breather/lump and three bell-shaped solitons,two breathers/lumps and a bell-shaped soliton,as well as mixing with one lump,one breather and a bell-shaped soliton are constructed from the 5-soliton solution.To study the behaviors that the obtained interaction solutions may have,we present some illustrative numerical simulations,which demonstrate that the choice of the parameters has a great impacts on the types of the solutions and their propagation properties.The method proposed can be effectively used to construct localized interaction solutions of many nonlinear evolution equations.The results obtained may help related experts to understand and study the interaction phenomena of nonlinear localized waves during propagations.展开更多
In this paper,we prove that there exists a unique local solution for the Cauchy problem of a system of the incompressible Navier-Stokes-Landau-Lifshitz equations with the Dzyaloshinskii-Moriya interaction and V-flow t...In this paper,we prove that there exists a unique local solution for the Cauchy problem of a system of the incompressible Navier-Stokes-Landau-Lifshitz equations with the Dzyaloshinskii-Moriya interaction and V-flow term inR^(2) and R^(3).Our methods rely upon approximating the system with a perturbed parabolic system and parallel transport.展开更多
In this paper, we construct a local supersonic flow in a 3-dimensional axis-symmetry nozzle when a uniform supersonic flow inserts the throat. We apply the local existence theory of boundary value problem for quasilin...In this paper, we construct a local supersonic flow in a 3-dimensional axis-symmetry nozzle when a uniform supersonic flow inserts the throat. We apply the local existence theory of boundary value problem for quasilinear hyperbolic system to solve this problem. The boundary value condition is set in particular to guarantee the character number condition. By this trick, the theory in quasilinear hyperbolic system can be employed to a large range of the boundary value problem.展开更多
This paper is concerned with the existence of global solutions to the Cauchy problem of a hyperbolic-parabolic coupled system with large initial data. To this end, we first construct its local solutions by the standar...This paper is concerned with the existence of global solutions to the Cauchy problem of a hyperbolic-parabolic coupled system with large initial data. To this end, we first construct its local solutions by the standard iteration technique, then we deduce the basic energy estimate by constructing a convex entropy-entropy flux pair to this system. Moreover, the L∞-estimates and H^2-estimates of solutions are obtained through some delicate estimates. In our results, we do not ask the far fields of the initial data to be equal and the initial data can be arbitrarily large which generalize the result obtained in [7].展开更多
In this paper, the aim is to establish the local existence of classical solutions for a class of compressible non-Newtonian fluids with vacuum in one-dimensional bounded intervals, under the assumption that the data s...In this paper, the aim is to establish the local existence of classical solutions for a class of compressible non-Newtonian fluids with vacuum in one-dimensional bounded intervals, under the assumption that the data satisfies a natural compatibility condition. For the results, the initial density does not need to be bounded below away from zero.展开更多
The authors of this article study the existence and uniqueness of weak so- lutions of the initial-boundary value problem for ut = div（（｜u｜^δ ＋ d0）｜↓△｜^p（x,t）-2↓△u） ＋ f（x, t） （0 〈 δ 〈 2）. They a...The authors of this article study the existence and uniqueness of weak so- lutions of the initial-boundary value problem for ut = div（（｜u｜^δ ＋ d0）｜↓△｜^p（x,t）-2↓△u） ＋ f（x, t） （0 〈 δ 〈 2）. They apply the method of parabolic regularization and Galerkin＇s method to prove the existence of solutions to the mentioned problem and then prove the uniqueness of the weak solution by arguing by contradiction. The authors prove that the solution approaches 0 in L^2 （Ω） norm as t →∞.展开更多
In this work,the localized method of fundamental solution(LMFS)is extended to Signorini problem.Unlike the traditional fundamental solution(MFS),the LMFS approximates the field quantity at each node by using the field...In this work,the localized method of fundamental solution(LMFS)is extended to Signorini problem.Unlike the traditional fundamental solution(MFS),the LMFS approximates the field quantity at each node by using the field quantities at the adjacent nodes.The idea of the LMFS is similar to the localized domain type method.The fictitious boundary nodes are proposed to impose the boundary condition and governing equations at each node to formulate a sparse matrix.The inequality boundary condition of Signorini problem is solved indirectly by introducing nonlinear complementarity problem function(NCP-function).Numerical examples are carried out to validate the reliability and effectiveness of the LMFS in solving Signorini problems.展开更多
We prove that n-dimensional radial symmetric Landau-Lifshitz equation possesses at least two classes of global smooth solutions with suitable initial-boundary conditions.
The results of this work deal with the existence and blow up of solutions for the following damped extensible beam with degenerate nonlocal damping and source term u_(tt)+Δ^(2)-M(||▽u||^(2))Δu+||Δu||^(2α)|u_(t)|^...The results of this work deal with the existence and blow up of solutions for the following damped extensible beam with degenerate nonlocal damping and source term u_(tt)+Δ^(2)-M(||▽u||^(2))Δu+||Δu||^(2α)|u_(t)|^(γ)u_(t)=|u|^(ρ)u.It is regarded as the second part of the paper by Narciso et al.(in 2023),where global existence,uniqueness and asymptotic stability of strong solutions were obtained for regular initial data in the case∣u∣^(ρ)u≡0.展开更多
We couple together existing ideas,existing results,special structure and novel ideas to accomplish the exact limits and improved decay estimates with sharp rates for all order derivatives of the global weak solutions ...We couple together existing ideas,existing results,special structure and novel ideas to accomplish the exact limits and improved decay estimates with sharp rates for all order derivatives of the global weak solutions of the Cauchy problem for an n-dimensional incompressible Navier-Stokes equations.We also use the global smooth solution of the corresponding heat equation to approximate the global weak solutions of the incompressible Navier-Stokes equations.展开更多
In this paper, the existence and uniqueness of the local generalized solution of the initial boundary value problem for a nonlinear hyperbolic equation are proved by the contraction mapping principle and the sufficien...In this paper, the existence and uniqueness of the local generalized solution of the initial boundary value problem for a nonlinear hyperbolic equation are proved by the contraction mapping principle and the sufficient conditions of blow_up of the solution in finite time are given.展开更多
The community diagnosis is an essential approach to the resolution of health problems with the involvement of the communities concerned who become object and subject. Improvingmaternal and child health is a health pri...The community diagnosis is an essential approach to the resolution of health problems with the involvement of the communities concerned who become object and subject. Improvingmaternal and child health is a health priority for many developing countries, including Mali. The objective was to study the role of community-based diagnosis in improving maternal and child protection in a vulnerable urban community in a developing country. Methodology: This was a research-action integrating a community diagnosis conducted in March 2023. The involvement of several stakeholders, including social actors including ASACO, membership card holders, district chiefs, neighborhood delegates, local authorities, and health professionals, made it possible to provide curative, preventive and promotional care. The ASACOSEKA Health Area was used as a setting for the study. The methodology was the indicator approach, contact, document review, interview of CSCOM patients, observation of the structure, prioritization of problems, development of an action plan and restitution of the report. Results: The monograph consisted of describing the characteristics of the study setting. Indeed, the ASACOSEKASI area is located on the left bank of the Niger River, with a population of 34,497 inhabitants. The CSCOM presented to describe a medical unit, a maternity unit, a laboratory unit, an ultrasound room and a medication storage room. The main pathologies found were confirmed simple malaria (45.08%), high AKI: 20.43%, confirmed severe malaria: 19.85%, suspected diarrhoea: 3.43%, trauma related to road accidents: 3.36%, pregnancy-related disorders (1%). BCG, Penta3, VAR, and yellow fever vaccination rates were above 100%. It reflects the fact that the doses administered were higher than the target population. This was related to out-of-area vaccination and lost doses. CPN1, CPN4, tetanus vaccination (VAT2) and family planning (FP) consultations all have a proportion above 100%. Maternal care is increased by out-of-area patients, particularly from Guinea. NPC3 and CPON have a proportion of less than 100%. The target population did not follow policies, standards and procedures. Postpartum, women rarely came to the CPON. Local actions to combat malaria included cleaning up plots and neighbourhoods, weeding families and streets, cleaning gutters, spraying the roosts of the female Anopheles Beetle, sleeping in LLINs, organising chemoprophylaxis days, promoting the use of MS, and using curtains against vectors. Conclusion: The community was involved at all stages of this diagnosis, from design to implementation, as well as to the restitution of local solutions. Indeed, the community diagnosis has led to a resolution plan related to reproductive health.展开更多
In this paper, we establish the global existence of the solution for the Landau-Lifshitz equation of the ferromagnetic spin chain. By Galerkin method, we first show the existence of the local solution for this equatio...In this paper, we establish the global existence of the solution for the Landau-Lifshitz equation of the ferromagnetic spin chain. By Galerkin method, we first show the existence of the local solution for this equation, and then by a priori estimates method, we extend the local solution to a global solution.展开更多
文摘In this paper,we prove the local existence and uniqueness of solutions to the evolutionary model for magnetoviscoelasticity in R^(2),R^(3).This model consists of an incompressible Navier-Stokes,a regularized system for the evolution of the deformation gradient and the Landau-Lifshitz-Gilbert system for the dynamics of the mag-netization.Our approach depends on approximating the system with a sequence of perturbed systems.
基金Supported by Key Project of Chinese Ministry of Education (Grant No.109140)the SWUFE's third period construction item funds of the 211 project (Grant No.211D3T06)
文摘The regularity of the Cauchy problem for a generalized Camassa-Holm type equation is investigated. The pseudoparabolic regularization approach is employed to obtain some prior estimates under certain assumptions on the initial value of the equation. The local existence of its solution in Sobolev space Hs （R） with 1 〈 s ≤ 3/2 is derived.
文摘In this paper,we study the existence of localized nodal solutions for Schrodinger-Poisson systems with critical growth{−ε^(2)Δv+V(x)v+λψv=v^(5)+μ|v|^(q−2)v,in R^(3),−ε^(2)Δψ=v^(2),in R^(3);v(x)→0,ψ(x)→0as|x|→∞.We establish,for smallε,the existence of a sequence of localized nodal solutions concentrating near a given local minimum point of the potential function via the perturbation method,and employ some new analytical skills to overcome the obstacles caused by the nonlocal term φu(x)=1/4π∫R^(3)u^(2)(y)/|x−y|dy.Our results improve and extend related ones in the literature.
基金supported by National Natural Science Foundation of China(11101295)
文摘We study the local analytic solutions f of the functional equation f（ψ（zf（z））） = φ（f（z）） for z in some neighborhood of the origin. Whether the solution f vanishes at z = 0 or not plays a critical role for local analytic solutions of this equation. In this paper, we obtain results of analytic solutions not only in the case f（0） = 0 but also for f（0） ≠ 0. When assuming f（0） = 0, for technical reasons, we just get the result for f′（0）≠ 0. Then when assuming f（0） = ω0 ≠ 0, ψ（0） = s # 0, ψ（z） is analytic at z = 0 and ψ（z） is analytic at z = ω0, we give the existence of local analytic solutions f in the case of 0 〈 ｜sω0｜ 〈 1 and the case of ｜sω0｜ = 1 with the Brjuno condition.
基金the Fundamental Research Funds for the Central Universities(Grants B200203009 and B200202126)the Natural Science Foundation of Jiangsu Province(Grant BK20190073)+2 种基金the State Key Laboratory of Acoustics,Chinese Academy of Sciences(Grant SKLA202001)the State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures,Shijiazhuang Tiedao University(Grant KF2020-22)the China Postdoctoral Science Foundation(Grants 2017M611669 and 2018T110430).
文摘A localized space-time method of fundamental solutions(LSTMFS)is extended for solving three-dimensional transient diffusion problems in this paper.The interval segmentation in temporal direction is developed for the accurate simulation of long-time-dependent diffusion problems.In the LSTMFS,the whole space-time domain with nodes arranged i divided into a series of overlapping subdomains with a simple geometry.In each subdomain,the conventional method of fundamental solutions is utilized and the coefficients associated with the considered domain can be explicitly determined.By calculating a combined sparse matrix system,the value at any node inside the space-time domain can be obtained.Numerical experi-ments demonstrate that high accuracy and efficiency can be simultaneously achieved via the LSTMFS,even for the problems defined on a long-time and quite complex computational domain.
文摘With the straification theory we have proved the transversal layer s 0 3,k (D) of complete equations for mixed fluid is not an empty set: s 0 3,k (D) ≠ for all k(k≥1) . Based on this conclusion and the “secondary equation” of s 0 3,k (D), this paper fully presents the expressions of coefficients in all local analytic solutions of the equations. Therefore we provide the calculation formulas by which we can get the numerical solutions to any desired accuracy.
基金Supported by the Zhejiang Provincial Natural Science Foundation of China under Grant No LQ13A010014the National Natural Science Foundation of China under Grant Nos 11326164,11401528,11435005 and 11375090+4 种基金the Global Change Research Program of China(No 2015CB953904)the Research Fund for the Doctoral Program of Higher Education of China(No 20120076110024)the Network Information Physics Calculation of Basic Research Innovation Research Group of China under Grant No 61321064Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things(No ZF1213)Shanghai Minhang District Talents of High Level Scientific Research Project
文摘By means of the modified Clarkson and Kruskal （CK） direct method and the variable separation approach, we investigate the （24-1）-dimensional Ito equation which was constructed by Ito in 1980. The full symmetry group with the Kac-Moody-Virasoro algebra structure and the variable separation solutions are obtained. By selecting appropriate arbitrary functions, some special soliton excitations are shown graphically. The results presented here would be beneficial for understanding the （2-t-1）-dimensional Ito equation better.
基金supported by the National Natural Science Foundation of China under grant No.11775116Jiangsu Qinglan highlevel talent Project。
文摘Based on a special transformation that we introduce,the N-soliton solution of the(2+1)-dimensional Boiti–Leon–Manna–Pempinelli equation is constructed.By applying the long wave limit and restricting certain conjugation conditions to the related solitons,some novel localized wave solutions are obtained,which contain higher-order breathers and lumps as well as their interactions.In particular,by choosing appropriate parameters involved in the N-solitons,two interaction solutions mixed by a bell-shaped soliton and one breather or by a bell-shaped soliton and one lump are constructed from the 3-soliton solution.Five solutions including two breathers,two lumps,and interaction solutions between one breather and two bell-shaped solitons,one breather and one lump,or one lump and two bell-shaped solitons are constructed from the4-soliton solution.Five interaction solutions mixed by one breather/lump and three bell-shaped solitons,two breathers/lumps and a bell-shaped soliton,as well as mixing with one lump,one breather and a bell-shaped soliton are constructed from the 5-soliton solution.To study the behaviors that the obtained interaction solutions may have,we present some illustrative numerical simulations,which demonstrate that the choice of the parameters has a great impacts on the types of the solutions and their propagation properties.The method proposed can be effectively used to construct localized interaction solutions of many nonlinear evolution equations.The results obtained may help related experts to understand and study the interaction phenomena of nonlinear localized waves during propagations.
文摘In this paper,we prove that there exists a unique local solution for the Cauchy problem of a system of the incompressible Navier-Stokes-Landau-Lifshitz equations with the Dzyaloshinskii-Moriya interaction and V-flow term inR^(2) and R^(3).Our methods rely upon approximating the system with a perturbed parabolic system and parallel transport.
文摘In this paper, we construct a local supersonic flow in a 3-dimensional axis-symmetry nozzle when a uniform supersonic flow inserts the throat. We apply the local existence theory of boundary value problem for quasilinear hyperbolic system to solve this problem. The boundary value condition is set in particular to guarantee the character number condition. By this trick, the theory in quasilinear hyperbolic system can be employed to a large range of the boundary value problem.
基金Huijiang Zhao was supported by the National Natural Science Foundation of China (10871151)Changjiang Zhu was supported by the National Natural Science Foundation of China (10625105 and 10431060)the Program for New Century Excellent Talentsin University (NCET-04-0745)
文摘This paper is concerned with the existence of global solutions to the Cauchy problem of a hyperbolic-parabolic coupled system with large initial data. To this end, we first construct its local solutions by the standard iteration technique, then we deduce the basic energy estimate by constructing a convex entropy-entropy flux pair to this system. Moreover, the L∞-estimates and H^2-estimates of solutions are obtained through some delicate estimates. In our results, we do not ask the far fields of the initial data to be equal and the initial data can be arbitrarily large which generalize the result obtained in [7].
基金Supported by NSFC(11201371,1331005)Natural Science Foundation of Shaanxi Province(2012JQ020)
文摘In this paper, the aim is to establish the local existence of classical solutions for a class of compressible non-Newtonian fluids with vacuum in one-dimensional bounded intervals, under the assumption that the data satisfies a natural compatibility condition. For the results, the initial density does not need to be bounded below away from zero.
基金Supported by NSFC (10771085)Graduate Innovation Fund of Jilin University(20111034)the 985 program of Jilin University
文摘The authors of this article study the existence and uniqueness of weak so- lutions of the initial-boundary value problem for ut = div（（｜u｜^δ ＋ d0）｜↓△｜^p（x,t）-2↓△u） ＋ f（x, t） （0 〈 δ 〈 2）. They apply the method of parabolic regularization and Galerkin＇s method to prove the existence of solutions to the mentioned problem and then prove the uniqueness of the weak solution by arguing by contradiction. The authors prove that the solution approaches 0 in L^2 （Ω） norm as t →∞.
基金supported by the National Science Foundation of China(No.52109089)support of Post Doctor Program(2019M652281)Nature Science Foundation of Jiangxi Province(20192BAB216040).
文摘In this work,the localized method of fundamental solution(LMFS)is extended to Signorini problem.Unlike the traditional fundamental solution(MFS),the LMFS approximates the field quantity at each node by using the field quantities at the adjacent nodes.The idea of the LMFS is similar to the localized domain type method.The fictitious boundary nodes are proposed to impose the boundary condition and governing equations at each node to formulate a sparse matrix.The inequality boundary condition of Signorini problem is solved indirectly by introducing nonlinear complementarity problem function(NCP-function).Numerical examples are carried out to validate the reliability and effectiveness of the LMFS in solving Signorini problems.
基金Supported by the National Natural Science Foundation of China under Grant No 10501006, and the China Post-Doctoral Science Foundation.
文摘We prove that n-dimensional radial symmetric Landau-Lifshitz equation possesses at least two classes of global smooth solutions with suitable initial-boundary conditions.
文摘The results of this work deal with the existence and blow up of solutions for the following damped extensible beam with degenerate nonlocal damping and source term u_(tt)+Δ^(2)-M(||▽u||^(2))Δu+||Δu||^(2α)|u_(t)|^(γ)u_(t)=|u|^(ρ)u.It is regarded as the second part of the paper by Narciso et al.(in 2023),where global existence,uniqueness and asymptotic stability of strong solutions were obtained for regular initial data in the case∣u∣^(ρ)u≡0.
文摘We couple together existing ideas,existing results,special structure and novel ideas to accomplish the exact limits and improved decay estimates with sharp rates for all order derivatives of the global weak solutions of the Cauchy problem for an n-dimensional incompressible Navier-Stokes equations.We also use the global smooth solution of the corresponding heat equation to approximate the global weak solutions of the incompressible Navier-Stokes equations.
文摘In this paper, the existence and uniqueness of the local generalized solution of the initial boundary value problem for a nonlinear hyperbolic equation are proved by the contraction mapping principle and the sufficient conditions of blow_up of the solution in finite time are given.
文摘The community diagnosis is an essential approach to the resolution of health problems with the involvement of the communities concerned who become object and subject. Improvingmaternal and child health is a health priority for many developing countries, including Mali. The objective was to study the role of community-based diagnosis in improving maternal and child protection in a vulnerable urban community in a developing country. Methodology: This was a research-action integrating a community diagnosis conducted in March 2023. The involvement of several stakeholders, including social actors including ASACO, membership card holders, district chiefs, neighborhood delegates, local authorities, and health professionals, made it possible to provide curative, preventive and promotional care. The ASACOSEKA Health Area was used as a setting for the study. The methodology was the indicator approach, contact, document review, interview of CSCOM patients, observation of the structure, prioritization of problems, development of an action plan and restitution of the report. Results: The monograph consisted of describing the characteristics of the study setting. Indeed, the ASACOSEKASI area is located on the left bank of the Niger River, with a population of 34,497 inhabitants. The CSCOM presented to describe a medical unit, a maternity unit, a laboratory unit, an ultrasound room and a medication storage room. The main pathologies found were confirmed simple malaria (45.08%), high AKI: 20.43%, confirmed severe malaria: 19.85%, suspected diarrhoea: 3.43%, trauma related to road accidents: 3.36%, pregnancy-related disorders (1%). BCG, Penta3, VAR, and yellow fever vaccination rates were above 100%. It reflects the fact that the doses administered were higher than the target population. This was related to out-of-area vaccination and lost doses. CPN1, CPN4, tetanus vaccination (VAT2) and family planning (FP) consultations all have a proportion above 100%. Maternal care is increased by out-of-area patients, particularly from Guinea. NPC3 and CPON have a proportion of less than 100%. The target population did not follow policies, standards and procedures. Postpartum, women rarely came to the CPON. Local actions to combat malaria included cleaning up plots and neighbourhoods, weeding families and streets, cleaning gutters, spraying the roosts of the female Anopheles Beetle, sleeping in LLINs, organising chemoprophylaxis days, promoting the use of MS, and using curtains against vectors. Conclusion: The community was involved at all stages of this diagnosis, from design to implementation, as well as to the restitution of local solutions. Indeed, the community diagnosis has led to a resolution plan related to reproductive health.
文摘In this paper, we establish the global existence of the solution for the Landau-Lifshitz equation of the ferromagnetic spin chain. By Galerkin method, we first show the existence of the local solution for this equation, and then by a priori estimates method, we extend the local solution to a global solution.
