Reaction-diffusion equations with spatially distributed hysteresis
Pavel Gurevich, Roman Shamin, Sergey Tikhomirov
TL;DR
This paper investigates reaction-diffusion equations with spatially varying hysteresis in the source term, establishing conditions for the existence, uniqueness, and stability of solutions in chemical and biological models.
Contribution
It introduces new mathematical conditions ensuring well-posedness of reaction-diffusion equations with spatial hysteresis, a novel aspect in modeling complex systems.
Findings
Proved existence of solutions under specific conditions.
Established uniqueness of solutions.
Demonstrated continuous dependence on initial data.
Abstract
The paper deals with reaction-diffusion equations involving a hysteretic discontinuity in the source term, which is defined at each spatial point. In particular, such problems describe chemical reactions and biological processes in which diffusive and nondiffusive substances interact according to hysteresis law. We find sufficient conditions that guarantee the existence and uniqueness of solutions as well as their continuous dependence on initial data.
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