Uniform Bounds for Solutions to Volume-Surface Reaction Diffusion Systems
Vandana Sharma, Jeff Morgan
TL;DR
This paper establishes criteria ensuring solutions to a volume-surface reaction-diffusion system remain uniformly bounded over time, addressing a complex interplay of boundary and interior reactions and diffusions.
Contribution
The paper introduces new criteria for uniform boundedness in volume-surface reaction-diffusion systems, expanding understanding of their long-term behavior.
Findings
Solutions are proven to be uniformly bounded under certain conditions.
The criteria apply to systems with boundary and interior reactions.
The results contribute to the stability analysis of reaction-diffusion models.
Abstract
We consider a reaction-diffusion system where some components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport. We establish criteria guaranteeing that solutions are uniformly bounded in time.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Nonlinear Partial Differential Equations · Mathematical and Theoretical Epidemiology and Ecology Models