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LOCAL EXISTENCE OF SOLUTION TO FREE BOUNDARY VALUE PROBLEM FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS 被引量:3
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作者 刘健 《Acta Mathematica Scientia》 SCIE CSCD 2012年第4期1298-1320,共23页
This paper is concerned with the free boundary value problem for multidimensional Navier-Stokes equations with density-dependent viscosity where the flow density vanishes continuously across the free boundary. Local ... This paper is concerned with the free boundary value problem for multidimensional Navier-Stokes equations with density-dependent viscosity where the flow density vanishes continuously across the free boundary. Local (in time) existence of a weak solution is established; in particular, the density is positive and the solution is regular away from the free boundary. 展开更多
关键词 Navier-Stokes equations free boundary value problem local existence
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LOCAL EXISTENCE AND UNIQUENESS OF STRONG SOLUTIONS TO THE TWO DIMENSIONAL NONHOMOGENEOUS INCOMPRESSIBLE PRIMITIVE EQUATIONS
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作者 Quansen JIU Fengchao WANG 《Acta Mathematica Scientia》 SCIE CSCD 2020年第5期1316-1334,共19页
In this article,we study the initial boundary value problem of the two-dimensional nonhomogeneous incompressible primitive equations and obtain the local existence and uniqueness of strong solutions.The initial vacuum... In this article,we study the initial boundary value problem of the two-dimensional nonhomogeneous incompressible primitive equations and obtain the local existence and uniqueness of strong solutions.The initial vacuum is allowed. 展开更多
关键词 local existence and uniqueness strong solutions nonhomogeneous incompressible primitive equations
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THE EXISTENCE AND LOCAL UNIQUENESS OF MULTI-PEAK SOLUTIONS TO A CLASS OF KIRCHHOFF TYPE EQUATIONS
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作者 崔磊磊 郭佳星 李工宝 《Acta Mathematica Scientia》 SCIE CSCD 2023年第3期1131-1160,共30页
In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate cri... In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate critical points of the potential function V(x),where a,b>0,1<p<5 are constants,andε>0 is a parameter.Applying the Lyapunov-Schmidt reduction method and a local Pohozaev type identity,we establish the existence and local uniqueness results of multi-peak solutions,which concentrate at{a_(i)}1≤i≤k,where{a_(i)}1≤i≤k are non-degenerate critical points of V(x)asε→0. 展开更多
关键词 Kirchhoff type equations potential functions having non-degenerate critical points the Lyapunov-Schmidt reduction method multi-peak solutions existence and local uniqueness
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Local Existence for Inhomogeneous Schrdinger Flow into Kihler Manifolds 被引量:3
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作者 Peter Y.H.Pang Hongyu WangDepartment of Mathematics,National University of Singapore,2 Science Drive 2,Republic of Singapore 117543Youde Wang Institute of Mathematics,Academy of Mathematics and System Sciences,Academia Sinica,Beijing,100080,P.R.China 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2000年第3期487-504,共18页
In this paper we show that there exists a unique local smooth solution for the Cauchy problem of the inhomogeneous Schrdinger flow for maps from a compact Riemannian manifold M with dim(M)≤3 into a compact Khler mani... In this paper we show that there exists a unique local smooth solution for the Cauchy problem of the inhomogeneous Schrdinger flow for maps from a compact Riemannian manifold M with dim(M)≤3 into a compact Khler manifold(N, J)with nonpositive Riemannian sectional curvature 展开更多
关键词 Inhomogeneous Schrdinger flow Khler manifold local existence
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On Local Existence and Blow-up of a Moving Boundary Problem in 1-D Chemotaxis Model 被引量:2
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作者 WU Shaohua WANG Chunying YUE Bo 《Journal of Partial Differential Equations》 CSCD 2016年第4期269-285,共17页
In this paper, the local existence and uniqueness of a chemotaxis model with a moving boundary are considered by the contraction mapping principle, and the explicit expression for the moving boundary is formulated. In... In this paper, the local existence and uniqueness of a chemotaxis model with a moving boundary are considered by the contraction mapping principle, and the explicit expression for the moving boundary is formulated. In addition, the finite-time blowup and chemotactic collapse of the solution for such kind of problem are discussed. 展开更多
关键词 Chemotaxis model moving boundary local existence finite-time blowup.
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具有奇异势和一般非线性的伪抛物方程解的局部存在性和爆破
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作者 江东月 唐忠华 房少梅 《Chinese Quarterly Journal of Mathematics》 2024年第2期111-127,共17页
In this paper,a semilinear pseudo-parabolic equation with a general nonlin-earity and singular potential is considered.We prove the local existence of solution by Galerkin method and contraction mapping theorem.Moreov... In this paper,a semilinear pseudo-parabolic equation with a general nonlin-earity and singular potential is considered.We prove the local existence of solution by Galerkin method and contraction mapping theorem.Moreover,we prove the blow-up of solution and estimate the upper bound of the blow-up time for J(u0)≤0.Finally,we prove the finite time blow-up and estimate the upper bound of blow-up time for J(u0)>0. 展开更多
关键词 Pseudo-parabolic equation Singular potential General nonlinearity local existence Blow-up time
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LOCAL WELL-POSEDNESS OF STRONG SOLUTIONS FOR THE NONHOMOGENEOUS MHD EQUATIONS WITH A SLIP BOUNDARY CONDITIONS 被引量:1
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作者 Hongmin LI Yuelong XIAO 《Acta Mathematica Scientia》 SCIE CSCD 2020年第2期442-456,共15页
This article is concerned with the 3 D nonhomogeneous incompressible magnetohydrodynamics equations with a slip boundary conditions in bounded domain.We obtain weighted estimates of the velocity and magnetic field,and... This article is concerned with the 3 D nonhomogeneous incompressible magnetohydrodynamics equations with a slip boundary conditions in bounded domain.We obtain weighted estimates of the velocity and magnetic field,and address the issue of local existence and uniqueness of strong solutions with the weaker initial data which contains vacuum states. 展开更多
关键词 Nonhomogeneous MHD equations local existence and uniqueness VACUUM t-weighted H^2 estimate Galerkin approximation
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LOCAL CLASSICAL SOLUTION OF FREE BOUNDARY PROBLEM FOR A COUPLED SYSTEM
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作者 王晓华 易法槐 杨舟 《Acta Mathematica Scientia》 SCIE CSCD 2005年第2期259-273,共15页
This paper considers a two-phase free boundary problem for coupled system including one parabolic equation and two elliptic equations. The problem comes from the discussion of a growth model of self-maintaining protoc... This paper considers a two-phase free boundary problem for coupled system including one parabolic equation and two elliptic equations. The problem comes from the discussion of a growth model of self-maintaining protocell in multidimensional case. The local classical solution of the problem with free boundary (?) y = g(x,t) between two domains is being seeked. The local existence and uniqueness of the problem will be proved in multidimensional case. 展开更多
关键词 local existence free boundary coupled system
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Existence for Semilinear Wave Equations with Low Regularity
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作者 YANG Ning YANG Han 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2006年第1期49-56,共8页
In this paper, we study how much regularity of initial data is needed to ensure existence of a local solution to the following semilinear wave equations utt-△u=F(u,Du) u(0,x)=f(x)∈H^s,δtu(0,x)=g(x)∈H^s-1... In this paper, we study how much regularity of initial data is needed to ensure existence of a local solution to the following semilinear wave equations utt-△u=F(u,Du) u(0,x)=f(x)∈H^s,δtu(0,x)=g(x)∈H^s-1,where F is quadratic in Du with D = (δr, δx1,…, δxn).We proved that the range of s is s ≥n+1/2 + δ, respectively, with δ 〉 1/4 if n = 2, and δ 〉 0 if n = 3, and δ ≥0 if n ≥ 4. Which is consistent with Lindblad's counterexamples [3] for n = 3, and the main ingredient is the use of the Strichartz estimates and the refinement of these. 展开更多
关键词 semilinear wave equations local existence low regularity
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Global Existence and Decay of Solution to Parabolic-Parabolic Keller-Segel Model in R^(d)
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作者 ZHONG Wenbin LIU Xiaofeng 《Journal of Donghua University(English Edition)》 CAS 2022年第1期85-94,共10页
We consider the global existence and decay of integral solutions to the parabolic-parabolic Keller-Segel system in d-dimension.On the one hand,by Banach fixed point theorem and some properties of heat kernel,we prove ... We consider the global existence and decay of integral solutions to the parabolic-parabolic Keller-Segel system in d-dimension.On the one hand,by Banach fixed point theorem and some properties of heat kernel,we prove the local existence and the global existence of integral solutions for the different initial data under some conditions that involve the size of the initial data.On the other hand,in the case of global solutions,we obtain their optimal time decay by Gronwall’s lemma. 展开更多
关键词 Keller-Segel system global existence integral solution local existence optimal time decay rate
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A Modified Transitional Korteweg-De Vries Equation: Posed in the Quarter Plane
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作者 Charles Bu 《Journal of Applied Mathematics and Physics》 2024年第7期2691-2701,共11页
This paper is concerned with a modified transitional Korteweg-de Vries equation ut+f(t)u2ux+uxxx=0, (x,t)∈R+×R+with initial value u(x,0)=g(x)∈H4(R+)and inhomogeneous boundary value u(0,t)=Q(t)∈C2([ 0,∞ )). Un... This paper is concerned with a modified transitional Korteweg-de Vries equation ut+f(t)u2ux+uxxx=0, (x,t)∈R+×R+with initial value u(x,0)=g(x)∈H4(R+)and inhomogeneous boundary value u(0,t)=Q(t)∈C2([ 0,∞ )). Under the conditions either 1) f(t)≤0, f′(t)≥0or 2) f(t)≤−αwhere α>0, we prove the existence of a unique global classical solution. 展开更多
关键词 Modified Transitional KdV Equation Initial-Boundary Value Problem Semi-Group local and Global existence
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Local and Global Existence of Solutions to Initial Value Problems of Modified Nonlinear Kawahara Equations 被引量:11
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作者 Shuang Ping TAO Shang Bin CUI 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2005年第5期1035-1044,共10页
This paper is devoted to studying the initial value problem of the modified nonlinear Kawahara equation the first partial dervative of u to t ,the second the third +α the second partial dervative of u to x ,the seco... This paper is devoted to studying the initial value problem of the modified nonlinear Kawahara equation the first partial dervative of u to t ,the second the third +α the second partial dervative of u to x ,the second the third +β the third partial dervative of u to x ,the second the thire +γ the fifth partial dervative of u to x = 0,(x,t)∈R^2.We first establish several Strichartz type estimates for the fundamental solution of the corresponding linear problem. Then we apply such estimates to prove local and global existence of solutions for the initial value problem of the modified nonlinear Karahara equation. The results show that a local solution exists if the initial function uo(x) ∈ H^s(R) with s ≥ 1/4, and a global solution exists if s ≥ 2. 展开更多
关键词 Kawahara equation Initial value problem SOLUTION local existence Global existence
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Local and Global Existence of Solutions to Initial Value Problems of Nonlinear Kaup-Kupershmidt Equations 被引量:6
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作者 Shuang Ping TAO Shang Bin CUI 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2005年第4期881-892,共12页
This paper is devoted to studying the initial value problems of the nonlinear Kaup Kupershmidt equations δu/δt + α1 uδ^2u/δx^2 + βδ^3u/δx^3 + γδ^5u/δx^5 = 0, (x,t)∈ E R^2, and δu/δt + α2 δu/δx ... This paper is devoted to studying the initial value problems of the nonlinear Kaup Kupershmidt equations δu/δt + α1 uδ^2u/δx^2 + βδ^3u/δx^3 + γδ^5u/δx^5 = 0, (x,t)∈ E R^2, and δu/δt + α2 δu/δx δ^2u/δx^2 + βδ^3u/δx^3 + γδ^5u/δx^5 = 0, (x, t) ∈R^2. Several important Strichartz type estimates for the fundamental solution of the corresponding linear problem are established. Then we apply such estimates to prove the local and global existence of solutions for the initial value problems of the nonlinear Kaup- Kupershmidt equations. The results show that a local solution exists if the initial function u0(x) ∈ H^s(R), and s ≥ 5/4 for the first equation and s≥301/108 for the second equation. 展开更多
关键词 Kaup-Kupershmidt equation Initial value problem SOLUTION local existence Global existence
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SOLVABILITY OF A PARABOLIC-HYPERBOLIC TYPE CHEMOTAXIS SYSTEM IN 1-DIMENSIONAL DOMAIN 被引量:6
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作者 陈化 吕文斌 吴少华 《Acta Mathematica Scientia》 SCIE CSCD 2016年第5期1285-1304,共20页
In this paper, we use contraction mapping principle, operator-theoretic approach and some uniform estimates to establish local solvability of the parabolic-hyperbolic type chemotaxis system with fixed boundary in 1-di... In this paper, we use contraction mapping principle, operator-theoretic approach and some uniform estimates to establish local solvability of the parabolic-hyperbolic type chemotaxis system with fixed boundary in 1-dimensional domain. In addition, local solvability of the free boundary problem is considered by straightening the free boundary. 展开更多
关键词 parabolic-hyperbolic system free boundary chemotaxis model local existence
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On Existence of Local Solutions of a Moving Boundary Problem Modelling Chemotaxis in 1-D 被引量:5
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作者 WU Shaohua YUE Bo 《Journal of Partial Differential Equations》 2014年第3期268-282,共15页
we prove the local existence and uniqueness of a moving boundary prob- lem modeling chemotactic phenomena. We also get the explicit representative for the moving boundary in a special case.
关键词 Keller-Segel model of chemotaxis moving boundary local existence special case.
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LOCAL AND GLOBAL EXISTENCE OF SOLUTIONS OF THE GINZBURG-LANDAU TYPE EQUATIONS
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作者 Zhou Fujun Cui Shangbin 《Journal of Partial Differential Equations》 2007年第3期220-246,共27页
This paper is devoted to studying the initial value problem of the Ginzburg-Landau type equations. We treat the case where the nonlinear interaction function is a general continuous function, not required to satisfy a... This paper is devoted to studying the initial value problem of the Ginzburg-Landau type equations. We treat the case where the nonlinear interaction function is a general continuous function, not required to satisfy any smoothness conditions. Local and global existence results of solutions of the problem are given. Decay estimates are also shown. 展开更多
关键词 Ginzburg-Landau type equations initial value problem local existence global existence.
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A Dirichlet Inhomogenous Boundary Value Problem for 1D Nonlinear Schrödinger Equation
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作者 Charles Bu 《Journal of Applied Mathematics and Physics》 2022年第3期656-660,共5页
Pure initial value problems for important nonlinear evolution equations such as nonlinear Schr&#246;dinger equation (NLS) and the Ginzburg-Landau equation (GL) have been extensively studied. However, many applicat... Pure initial value problems for important nonlinear evolution equations such as nonlinear Schr&#246;dinger equation (NLS) and the Ginzburg-Landau equation (GL) have been extensively studied. However, many applications in physics lead to mathematical models where boundary data is inhomogeneous, e.g. in radio frequency wave experiments. In this paper, we investigate the mixed initial-boundary condition problem for the nonlinear Schr&#246;dinger equation iu<sub>t</sub> = u<sub>xx</sub> – g|u|<sup>p-1</sup>u, g &#8712;R, p > 3 on a semi-infinite strip. The equation satisfies an initial condition and Dirichlet boundary conditions. We utilize semi-group theory to prove existence and uniqueness theorem of a strong local solution. 展开更多
关键词 Nonlinear Schrödinger Equation Inhomogeneous Boundary Condition local existence and Uniqueness
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Local Schrodinger flow into Kahler manifolds 被引量:7
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作者 丁伟岳 王友德 《Science China Mathematics》 SCIE 2001年第11期1446-1464,共19页
In this paper we show that there exists a unique local smooth solution for the Cauchy problem of the Schrodinger flow for maps from a compact Riemannian manifold into a complete Kahler manifold, or from a Euclidean sp... In this paper we show that there exists a unique local smooth solution for the Cauchy problem of the Schrodinger flow for maps from a compact Riemannian manifold into a complete Kahler manifold, or from a Euclidean space Rm into a compact Kahler manifold. As a consequence, we prove that Heisenberg spin system is locally well-posed in the appropriate Sobolev spaces. 展开更多
关键词 Schriidinger flow Heisenberg spin system local existence Kahler manifold.
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The Regularity of Local Solutions for a Generalized Camassa-Holm Type Equation
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作者 Shao Yong LAI Jian ZHANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2009年第12期2065-2076,共12页
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
关键词 existence of local solutions Camassa-Holm type equation dissipative term pseudoparabolic regularization method
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Blow-up of Solutions for a Time-space Fractional Evolution System 被引量:1
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作者 Yong Qiang XU Zhong TAN 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2013年第6期1067-1074,共8页
In this paper, firstly, we study the local existence and uniqueness of mild solutions for fractional evolution systems with nonlocal in time nonlinearity. Then, we claim that such a mild solution is weak solution of t... In this paper, firstly, we study the local existence and uniqueness of mild solutions for fractional evolution systems with nonlocal in time nonlinearity. Then, we claim that such a mild solution is weak solution of this system. Finally, we prove a blow-up result under some conditions. 展开更多
关键词 local existence fractional integrals and derivatives evolution systems
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