On the Positivity of Weak Solutions to a Class of Cross Diffusion Systems
Dung Le
TL;DR
This paper proves that weak solutions to certain cross diffusion systems, inspired by biological models, remain positive, with conditions that are nearly optimal, supported by examples and counterexamples.
Contribution
It establishes positivity conditions for weak solutions to cross diffusion systems, extending the understanding of the SKT model in population biology.
Findings
Positivity of weak solutions under specific conditions
Examples demonstrating the near optimality of conditions
Counterexamples showing limitations of positivity
Abstract
We establish the positivity 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. Examples and counterexamples will be provided to show that our contions are near optimal.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical and Theoretical Epidemiology and Ecology Models · Mathematical Biology Tumor Growth · Nonlinear Differential Equations Analysis