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1.
The author discussed a class of singularly perturbed problems for differential equation fiee {1--7]). Now we consider the non1ocal singu1arly perturbed problem as follows:where E is a positive small parameter anHere x = (xl, x2,' ) x.) E n, fl denotes a bounded region in R", 0fl signilies a boundary offl for class Cl cr (cr 6 (0, 1) is H5lder exponent), T0 is a positive constant, L1 is a uniformlyelliptic operator, L2 is a first order differential operator, T is an integral operator, K(x…  相似文献
2.
THE NONLOCAL INITIAL PROBLEMS OF A SEMILINEAR EVOLUTION EQUATION   总被引:1,自引:0,他引:1  
The purpose of this paper is to investigate the existence of solutions to a nonlocal Cauchy problem for an evolution equation. The methods used here include the semigroup methods in proper spaces and Schauder's theorem. And the results are applied to a system of nonlinear partial differential equations with nonlinear boundary conditions.  相似文献
3.
Recently much work has been devoted to nonlocal problems. However, very little has been accomplished in the literature for nonlocal initial problems with nonlinear boundary conditions. It is the purpose of this paper to prove the existence results for solutions to a semilinear parabolic PDE with linear homogeneous boundary conditions, and to other ones with nonlinear boundary conditions, provided the ordered upper and lower solutions are given. Semigroup, fractional order function spaces and generalized Poincaré operators play an important role in proving the existence of solutions. Supportedpartly by Research Grant 19531060 of China NSF and Grant 97024811 of the Foundation of Doctoral Program  相似文献
4.
This paper deals with the blow-up properties of the solution to the degenerate nonlinear reaction diffusion equation with nonlocal source in subject to the homogeneous Dirichlet boundary conditions. The existence of a unique classical nonnegative solution is established and the sufficient conditions for the solution exists globally or blows up in finite time are obtained. Furthermore, it is proved that under certain conditions the blow-up set of the solution is the whole domain.

  相似文献

5.
In this paper, the problems of the nonlocal initial conditions for the singularly perturbed reaction diffusion systems are considered. Under suitable conditions, using the comparison theorem the asymptotic behavior of solutions for the initial boundary value problems are studied.  相似文献
6.
1991MRSubjectClassification35B2535K57Theauthorsstudiedakilldofsingularlypertllrbedproblemsin[1]-[61.Nowwe't()llsiderthefollowingsingularlyperturbedproblemforthenonlocalboulldaryconditionsouteof~Li'Ui=.fi(X,.UljUZj',JINN,~),0相似文献
7.
莫嘉琪 《应用数学》1997,10(4):111-113
本文研究了一类非局部反应扩散问题.利用上、下解,讨论了相应问题解的存在唯一性及其渐近性态.  相似文献
8.
We obtain sign changing solutions of a class of nonlocal quasilinear elliptic boundary value problems using variational methods and invariant sets of descent flow.  相似文献
9.
In this paper, we study a nonlocal variational inequality. The nonlocality appears both in the coefficients of the operator, through an integral representing some elastic energy, and in the constraints, which are of the type called soft in the literature.  相似文献
10.
In this paper, we consider a nonlocal problem with integral conditions for the quasilinear hyperbolic equation in a rectangular domain. The existence and uniqueness of the generalized solution are established.  相似文献
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