多物种种群的超线性非局部扩散系统：适定性与离散链式法则
Superlinear nonlocal diffusion systems for multispecies populations: well-posedness and discrete chain rules
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中文总结 AI 辅助
本文研究逼近SKT模型的多物种非局部扩散系统，通过熵不等式和新的离散链式法则证明强解的全局存在唯一性，并用于构造保结构有限体积格式，数值模拟验证非局部到局部极限。
中文摘要 AI 辅助
本文在有界域内分析了一个描述多物种种群动力学并逼近Shigesada-Kawasaki-Teramoto (SKT)模型的非局部扩散系统。该模型由一组Andreu-Mazón-Rossi-Toledo型积分微分方程组成，其中非局部交叉扩散算子作用于非线性扩散势。我们建立了强解的全局存在性和唯一性。存在性证明依赖于由熵不等式推导出的合适的先验估计，而该不等式的证明需要发展新的离散链式法则不等式。作为副产品，这些不等式为相应的局部SKT系统构造保结构有限体积格式提供了基础。解的唯一性通过对偶论证建立。最后，一维数值模拟展示了非局部到局部的极限以及超线性和次线性扩散势下解的定性行为。
英文摘要
A nonlocal diffusion system describing the dynamics of multi-species populations and approximating the Shigesada-Kawasaki-Teramoto (SKT) model is analyzed in a bounded domain. The model consists of a system of integro-differential equations of Andreu-Mazón-Rossi-Toledo type, in which a nonlocal cross-diffusion operator acts on nonlinear diffusion potentials. We establish the global existence and uniqueness of strong solutions. The existence proof relies on suitable a priori estimates derived from an entropy inequality, whose proof requires the development of novel discrete chain-rule inequalities. As a by-product, these inequalities provide the basis for the construction of structure-preserving finite-volume schemes for the corresponding local SKT system. Uniqueness of solutions is established by means of a duality argument. Finally, one-dimensional numerical simulations illustrate the nonlocal-to-local limit and the qualitative behavior of solutions for superlinear and sublinear diffusion potentials.
发表机构
- TU Wien（维也纳工业大学）
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