共查询到20条相似文献,搜索用时 15 毫秒
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This paper discusses the generalized DaveyStewartsonsystem. By constructing a cross-constrained variational problemand so-called invariant manifolds of the evolution flow, wederive a sharp criterion for blow-up and global existence ofthe solutions. 相似文献
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《Mathematical Methods in the Applied Sciences》2018,41(10):3718-3749
This paper deals with the existence and uniqueness of the global solutions to the initial boundary value problem for a generalized Zakharov system with direct self‐interaction of the dispersive waves and weak dissipation in the nondispersive subsystem. We prove the global existence of the generalized solution to the problem by a priori estimates and Galerkin method. We also establish the regularity of the global generalized solution and the existence and uniqueness of the global classical solution. Moreover, we obtain the convergence of the solutions of the generalized Zakharov system with dissipation as the dissipative coefficient approaches zero. 相似文献
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三维复Ginzburg-Landau方程的整体解的存在惟一性 总被引:2,自引:0,他引:2
在三维空间中研究带2σ次非线性项的复值Ginzburg—Landau方程(CGL) ut=ρu (1 iγ)△u-(1 iμ)|u|^2σu,通过先验估计的方法,在适当的σ的假设下,获得该方程周期边值问题整体解的存在性和惟一性. 相似文献
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Global existence and asymptotic behavior of solution for Rosenau equation with Stokes damped term 下载免费PDF全文
We study the small‐data Cauchy problem for n‐dimensional Stokes damped Rosenau equation. Under some assumptions, we prove the global existence and uniqueness of the small‐amplitude solution by utilizing the contraction mapping principle and study the asymptotic behavior of the solution. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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Venkatasubramaniam Bhuvaneswari Lingeshwaran Shangerganesh Krishnan Balachandran 《Mathematical Methods in the Applied Sciences》2015,38(17):3738-3746
In this paper, we study the global existence of solution for the quasilinear chemotaxis system with Dirichlet boundary conditions, and further we show that the blow up properties of the solution depend only on the first eigenvalue. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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Global existence of solution of Cauchy problem for nonlinear pseudo-parabolic equation 总被引:1,自引:0,他引:1
In this paper, we prove that the Cauchy problem for the nonlinear pseudo-parabolic equation
vt−αvxxt−βvxx+γvx+fx(v)=φx(vx)+g(v)−αg(v)xx 相似文献
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In this paper,we consider the global existence of solutions for the Cauchy problem of the generalized sixth order bad Boussinesq equation.Moreover,we show that the supremum norm of the solution decays algebraically to zero as(1+t)(1/7)when t approaches to infnity,provided the initial data are sufciently small and regular. 相似文献
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Global Existence of Smooth Solutions to Three Dimensional Hall-MHD System with Mixed Partial Viscosity 下载免费PDF全文
Yuzhu Wang 《偏微分方程(英文版)》2021,34(1):1-13
We investigate the global existence of smooth solutions to the three dimensional generalized Hall-MHD system with mixed partial viscosity in this work. The
diffusion of mixed partial viscosity is weaker than that of full viscosity, which cases
new difficulty in proving global smooth solutions. Moreover, Hall term heightens the
level of nonlinearity of the standard MHD system. Global smooth solutions are established by using energy method and the bootstrapping argument, provided that the
initial data is enough small. 相似文献
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ThisresearchissupportedbytheNationalNaturalScienceFoundationofChina.1.IntroductionInthispaper,weconsiderthefollowinginitial--boundaryvalueproblemwhereQ~fix(o,co),aQ=aflx(o,co),fiisaboundeddomaininEuclideanspaceR"(n22)withsmoothboundaryonandac=(u.,,'Iu..)denotesthegradientoffunctionu(x).Weassumethefunctionsal(x,t,u,p)(i=1,2,',n)anda(x,t,u,p)arelocallyH5ldercontinuousonfix(0,co)suchthatwherealtuandparepositiveconstants,m,aZIa3.hi,b2,alIadZ20,or321areconstants,m*E[0,m 2),hi16z/0,afl m*/… 相似文献
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Yuxiang Li Weibing Deng Chunhong Xie 《Proceedings of the American Mathematical Society》2002,130(12):3661-3670
The initial-boundary value problems are considered for the strongly coupled degenerate parabolic system
in the cylinder , where is bounded and are positive constants. We are concerned with the global existence and nonexistence of the positive solutions. Denote by the first Dirichlet eigenvalue for the Laplacian on . We prove that there exists a global solution iff .
in the cylinder , where is bounded and are positive constants. We are concerned with the global existence and nonexistence of the positive solutions. Denote by the first Dirichlet eigenvalue for the Laplacian on . We prove that there exists a global solution iff .
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§ 1 IntroductionInthispaperwediscusstheglobalclassicalsolutionofamultidimensionalquasistationaryproblem .Theproblemcomesfromthediscussionofagrowthmodelofselfmaintainingprotocell(see [1— 3])inmultidimensionalcase .Theprotocellcanbevisualizedashavingaporousst… 相似文献
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In this paper, the existence and the uniqueness of the global solution for the Cauchy problem of the multidimensional generalized Boussinesq equation are obtained. Furthermore, the blow‐up of the solution for the Cauchy problem of the generalized Boussinesq equation is proved. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
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In this paper, we investigate the global existence of solutions to a hyperbolic-parabolic model of chemotaxis arising in the theory of reinforced random walks. To get -estimates of solutions, we construct a nonnegative convex entropy of the corresponding hyperbolic system. The higher energy estimates are obtained by the energy method and a priori assumptions.
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The existence and uniqueness of the global generalized solution and the global classical solution to the initial boundary value problem for a system of generalized IMBq equations are proved. This paper also arrives at some sufficient conditions of blow up of the solution in finite time. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
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Lin Zhi Yu Jian 《高校应用数学学报(英文版)》2007,22(4):497-504
By using Fort theorem the generic stability result for the system of generalized vector equilibrium problems is established.Further,by proving the existence and connectivity of minimal essential set the existence result of essential components in the solution set is derived. 相似文献