Effect of external potentials in a coupled system of multi-component incongruent diffusion
Effect of external potentials in a coupled system of multi-component incongruent diffusion
复制标题
多组分不一致扩散耦合系统中外部电势的影响
DOI：
10.12775/tmna.2019.066
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发表时间：
2019-11
影响因子：
0.7
通讯作者：
Tian Xu
中科院分区：
文献类型：
--
作者：
Yanheng Ding;Tian Xu
本文研究了一类形式为[Partial_tz=\mathbf{D}\Delta_xz+M(X)z+W(X)|z|^{p-2}\beta z，\quad z\冒号\mathbb R^N\to\mathbb R^{2K}，\N\geq2]形式的多组分反应扩散系统，其中$M$，$W$分别是扩散系数矩阵和耦合常数矩阵。当扩散速率较小时，外势函数的几何形状会影响系统解的多解性。有趣的是，对于$z=(u，v)$，我们将处理标准扩散系数$D_u和不协调扩散系数$D_v<；0，这在反应扩散系统的研究中通常被忽略。
This work is devoted to investigations of some interesting aspects of a multi-component Reaction-Diffusion system of the form \[ \partial_t z=\mathbf{D}\Delta_x z + M(x)z + W(x)|z|^{p-2}\beta z, \quad z\colon \mathbb R\times\mathbb R^N\to\mathbb R^{2K}, \ N\geq2 \] where $M$, $W$ are external potential functions, $\mathbf{D}$ and $\bt$ are matrices of diffusion coefficients and coupling constants respectively. When the diffusion rate is small, we show that the geometric shapes of the external potential functions will influence the multiplicity of solutions to the system. It is also of interest to know that, for $z=(u,v)$, we shall deal with standard diffusion coefficients $D_u> 0$ and the incongruent diffusion coefficients $D_v< 0$ which has generally been overlooked in the study of Reaction-Diffusion systems.