共查询到20条相似文献,搜索用时 46 毫秒
1.
In this paper we consider a class of nonlinear elliptic problems of the type
$
\left\{ \begin{gathered}
- div(a(x,\nabla u)) - div(\Phi (x,u)) = fin\Omega \hfill \\
u = 0on\partial \Omega , \hfill \\
\end{gathered} \right.
$
\left\{ \begin{gathered}
- div(a(x,\nabla u)) - div(\Phi (x,u)) = fin\Omega \hfill \\
u = 0on\partial \Omega , \hfill \\
\end{gathered} \right.
相似文献
2.
More work is done to study the explicit, weak and strong implicit difference solution for the first boundary problem of quasilinear parabolic system: $$\begin{gathered} u_t = ( - 1)^{M + 1} A(x,t,u, \cdots ,u_x M - 1)u_x 2M + f(x,t,u, \cdots u_x 2M - 1), \hfill \\ (x,t) \in Q_T = \left| {0< x< l,0< t \leqslant T} \right|, \hfill \\ u_x ^k (0,t) = u_x ^k (l,t) = 0 (k = 0,1, \cdots ,M - 1),0< t \leqslant T, \hfill \\ u(x,0) = \varphi (x),0 \leqslant x \leqslant l, \hfill \\ \end{gathered} $$ whereu, ?, andf arem-dimensional vector valued functions, A is anm×m positively definite matrix, and $u_t = \frac{{\partial u}}{{\partial t}},u_x ^k = \frac{{\partial ^k u}}{{\partial x^k }}$ . For this problem, the convergence of iteration for the general difference schemes is proved. 相似文献
3.
In this article, we study the homogenization of the family of parabolic equations over periodically perforated domains
4.
Another method for computing the densities of integrals of motion for the Korteweg-de Vries equation
B. M. Levitan 《Mathematical Notes》1977,22(1):562-565
In the first section of this article a new method for computing the densities of integrals of motion for the KdV equation is given. In the second section the variation with respect to q of the functional ∫ 0 π w (x,t,x,;q)dx (t is fixed) is computed, where W(x, t, s; q) is the Riemann function of the problem $$\begin{gathered} \frac{{\partial ^z u}}{{\partial x^2 }} - q(x)u = \frac{{\partial ^2 u}}{{\partial t^2 }} ( - \infty< x< \infty ), \hfill \\ u|_{t = 0} = f(x), \left. {\frac{{\partial u}}{{\partial t}}} \right|_{t = 0} = 0. \hfill \\ \end{gathered} $$ 相似文献
5.
6.
Robert Černý 《Applications of Mathematics》2013,58(5):555-593
Let Ω ? ? n , n ? 2, be a bounded connected domain of the class C 1,θ for some θ ∈ (0, 1]. Applying the generalized Moser-Trudinger inequality without boundary condition, the Mountain Pass Theorem and the Ekeland Variational Principle, we prove the existence and multiplicity of nontrivial weak solutions to the problem $$\begin{gathered} u \in W^1 L^\Phi \left( \Omega \right), - div\left( {\Phi '\left( {\left| {\nabla u} \right|} \right)\frac{{\nabla u}} {{\left| {\nabla u} \right|}}} \right) + V\left( x \right)\Phi '\left( {\left| u \right|} \right)\frac{u} {{\left| u \right|}} = f\left( {x,u} \right) + \mu h\left( x \right) in \Omega , \hfill \\ \frac{{\partial u}} {{\partial n}} = 0 on \partial \Omega , \hfill \\ \end{gathered}$$ where Φ is a Young function such that the space W 1 L Φ(Ω) is embedded into exponential or multiple exponential Orlicz space, the nonlinearity f(x, t) has the corresponding critical growth, V (x) is a continuous potential, h ∈ (L Φ(Ω))* is a nontrivial continuous function, µ ? 0 is a small parameter and n denotes the outward unit normal to ?Ω. 相似文献
7.
F. Andreu J. M. Mazon J. Toledo 《NoDEA : Nonlinear Differential Equations and Applications》1995,2(3):267-289
This paper is primarily concerned with the large time behaviour of solutions of the initial boundary value problem $$\begin{gathered} u_t = \Delta \phi (u) - \varphi (x,u)in\Omega \times (0,\infty ) \hfill \\ - \frac{{\partial \phi (u)}}{{\partial \eta }} \in \beta (u)on\partial \Omega \times (0,\infty ) \hfill \\ u(x,0) = u_0 (x)in\Omega . \hfill \\ \end{gathered} $$ Problems of this sort arise in a number of areas of science; for instance, in models for gas or fluid flows in porous media and for the spread of certain biological populations. 相似文献
8.
The initial boundary value problem
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