Solutions of a system of diffusion equations |
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| Authors: | Yanheng Ding Shixia Luan Michel Willem |
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| Institution: | 1. Institute of Mathematics, AMSS, Chinese Academy of Sciences, 100080, Beijing, China
2. Department of Mathematics, Qufu Normal University, 273165, Shandong, China
3. Départment de Mathématiques pures et appliquées, Université Catholique de Louvain, 1348, Louvain-La-Neuve, Belgium
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| Abstract: | We study existence and multiplicity of homoclinic type solutions to the following system of diffusion equations on
\mathbbR ×W{\mathbb{R}} \times \Omega
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$
\left\{ {{*{20}c}
{\,\,{\partial}_t u - {\Delta}_x u + b(t,x) \cdot {\nabla}_x u + V(x)u = H_v (t,x,u,v),} \\
{ - {\partial}_t v - {\Delta}_x v - b(t,x) \cdot {\nabla}_x v + V(x)v = H_u (t,x,u,v),}\\
} \right.
$
\left\{ {\begin{array}{*{20}c}
{\,\,{\partial}_t u - {\Delta}_x u + b(t,x) \cdot {\nabla}_x u + V(x)u = H_v (t,x,u,v),} \\
{ - {\partial}_t v - {\Delta}_x v - b(t,x) \cdot {\nabla}_x v + V(x)v = H_u (t,x,u,v),}\\
\end{array} } \right.
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| Keywords: | |
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