Relative compactness in $L^p$ of solutions of some 2m components competition-diffusion systems
Relative compactness in $L^p$ of solutions of some 2m components competition-diffusion systems
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DOI：
10.3934/dcds.2008.21.233
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发表时间：
2008-02
影响因子：
1.1
通讯作者：
D. Hilhorst;M. Iida;M. Mimura;H. Ninomiya
中科院分区：
文献类型：
--
作者：
D. Hilhorst;M. Iida;M. Mimura;H. Ninomiya
考虑了一类2 m元抛物型方程和m元常微分方程的竞争扩散方程组，证明了当反应系数趋于无穷大时，每个分量的子序列在L^p中的强收敛性.在$4$组件的特殊情况下，该系统的解决方案收敛到Stefan问题。
We consider a class of $2m$ components competition-diffusion systems which involve $m$ parabolic equations as well as $m$ ordinary differential equation, and prove the strong convergence in $L^p$ of a subsequence of each component as the reaction coefficient tends to infinity. In the special case of $4$ components the solution of this system converges to that of a Stefan problem.