共查询到20条相似文献,搜索用时 15 毫秒
1.
Christer Borell 《Probability Theory and Related Fields》1991,87(3):403-409
Suppose a, b, and are reals witha<b and consider the following diffusion equation
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2.
This paper is concerned with the Cauchy problem for the nonlinear parabolic equation $${\partial _t}u| = \vartriangle u + F(x,t,u,\nabla u){\text{ in }}{{\text{R}}^N} \times (0,\infty ),{\text{ }}u(x,0) = \varphi (x){\text{ in }}{{\text{R}}^N},$$ , where $$\begin{gathered} N \geqslant 1, \hfill \\ F \in C(R^N \times (0,\infty ) \times R \times R^N ), \hfill \\ \phi \in L^\infty (R^N ) \cap L^1 (R^N ,(1 + |x|^K )dx)forsomeK \geqslant 0 \hfill \\ \end{gathered} $$ . We give a sufficient condition for the solution to behave like a multiple of the Gauss kernel as t → ∞ and obtain the higher order asymptotic expansions of the solution in W 1,q (R N ) with 1 ≤ q ≤ ∞. 相似文献
3.
The authors study the existence of homoclinic type solutions for the following system of diffusion equations on R × RN:{■tu-xu + b ·▽xu + au + V(t,x)v = Hv(t,x,u,v),-■tv-xv-b·▽xv + av + V(t,x)u = Hu(t,x,u,v),where z =(u,v):R × RN → Rm × Rm,a > 0,b =(b1,···,bN) is a constant vector and V ∈ C(R × RN,R),H ∈ C1(R × RN × R2m,R).Under suitable conditions on V(t,x) and the nonlinearity for H(t,x,z),at least one non-stationary homoclinic solution with least energy is obtained. 相似文献
4.
Shuang-jie Peng 《应用数学学报(英文版)》2006,22(1):137-162
Abstract Let Ω be the unit ball centered at the origin in
. We study the following problem
5.
In this paper we consider the weakly coupled elliptic system with critical growth
6.
In the present paper, the following Dirichlet problem and Neumann problem involving the p-Laplacian
7.
Wu Shaoping 《数学学报(英文版)》1991,7(1):4-12
LetL be a self-adjoint linear operator andN be the gradient of a functional ϕ, which is almost quadratic. We first give a theorem on the surjectivity of the operatorL+N, then apply the result to semilinear elliptic systems:
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