Analysis of a Multidimensional Parabolic Population Model with Strong Cross-Diffusion
Analysis of a Multidimensional Parabolic Population Model with Strong Cross-Diffusion
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DOI：
10.1137/s0036141003427798
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
Li Chen;A. Jüngel
中科院分区：
文献类型：
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作者：
Li Chen;A. Jüngel
证明了两个竞争物种的多维抛物型强耦合模型的非负弱解的整体存在性。该模型的主要特征是扩散矩阵是非对称的，通常不是正定的，并且允许非对角矩阵元素（交叉扩散项）是“大”的。存在性证明的思想是使用有限差分对交叉扩散项进行仔细的近似，并使用产生先验估计的熵不等式。
The global existence of a nonnegative weak solution to a multidimensional parabolic strongly coupled model for two competing species is proved. The main feature of the model is that the diffusion matrix is nonsymmetric and generally not positive definite and that the nondiagonal matrix elements (the cross-diffusion terms) are allowed to be "large." The ideas of the existence proof are a careful approximation of the cross-diffusion terms using finite differences and the use of an entropy inequality yielding a priori estimates.