SPLITTING SCHEMES AND SEGREGATION IN REACTION CROSS-DIFFUSION SYSTEMS
SPLITTING SCHEMES AND SEGREGATION IN REACTION CROSS-DIFFUSION SYSTEMS
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DOI：
10.1137/17m1158379
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发表时间：
2018-01-01
影响因子：
2
通讯作者：
Schmidtchen, M.
中科院分区：
文献类型：
--
作者：
Carrillo, J. A.;Fagioli, S.;Schmidtchen, M.
在反应扩散系统中观察到的最令人着迷的现象之一是分离溶液的出现，即，人口密度与不相交的支持。我们分析了这样一个反应交叉扩散系统。为了在不限制支集或正性的情况下证明一类初值的弱解的存在性，我们提出了一种将常微分方程与最优迁移方法相结合的变分分裂格式.此外，这种方法使我们能够证明保守的隔离最初隔离的数据，即使在真空的存在下。
One of the most fascinating phenomenon observed in reaction diffusion systems is the emergence of segregated solutions, i.e., population densities with disjoint supports. We analyze such a reaction cross-diffusion system. In order to prove existence of weak solutions for a wide class of initial data without restriction of their supports or their positivity, we propose a variational splitting scheme combining ODEs with methods from optimal transport. In addition, this approach allows us to prove conservation of segregation for initially segregated data even in the presence of vacuum.