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arXiv · 1906.03456

Uniqueness and Regularity of Unbounded Weak Solutions to a Class of Cross Diffusion Systems

Dung Le
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Abstract

We establish the uniqueness and regularity of weak (and very weak) solutions to a class of cross diffusion systems which is inspired by models in mathematical biology/ecology, in particular the Shigesada-Kawasaki-Teramoto (SKT) model in population biology. No boundedness assumption on these solutions is supposed here as known techniques for scalar equations such as maximum/comparison principles are generally unavailable for systems. Furthermore, for planar domains we show that unbounded weak solutions satisfying mild integrability conditions are in fact smooth.

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Dung Le. 2019-06-08. Uniqueness and Regularity of Unbounded Weak Solutions to a Class of Cross Diffusion Systems. https://arxiv.org/abs/1906.03456

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