Analysis and numerical solution of a nonlinear cross-diffusion system arising in population dynamics
Analysis and numerical solution of a nonlinear cross-diffusion system arising in population dynamics
复制标题
种群动态中非线性交叉扩散系统的分析与数值求解
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
A. Jüngel
中科院分区：
文献类型：
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作者：
G. Galiano;M. Garzón;A. Jüngel
研究了一类具有交叉扩散项的两种群竞争非线性种群模型的解析解和数值解。由于交叉扩散项，问题是强非线性的，因此，没有最大值原理通常适用。首先证明了在任意空间维上抛物方程组弱解的存在性。然后，一维平稳问题进行了研究分析和隔离的概念进行了讨论。最后，我们提出了数值计算结果的一维固定问题强调隔离的物种的影响。
A nonlinear population model with cross-diffusion terms for two competing species is studied analytically and numerically. Due to the cross diffusion terms, the problem is strongly nonlinear and so, no maximum principle generally applies. We show first the existence of weak solutions to the parabolic system in any space dimension. Then the one-dimensional stationary problem is investigated analytically and the notion of segregation is discussed. Finally, we present numerical results for the one-dimensional stationary problem underlining the effects of segregation of the species.