Reaction-diffusion equations with spatially distributed hysteresis
arXiv:1205.3580 · doi:10.1137/120879889
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.
30 pages, 14 figures
References in corpus (1)
Cited by in corpus (4)
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- Generalized Play Hysteresis Operators in Limits of Fast-Slow Systems
- Hysteresis and phase transitions in a lattice regularization of an ill-posed forward-backward diffusion equation
- Spatially discrete reaction-diffusion equations with discontinuous hysteresis