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Reaction-diffusion equations with spatially distributed hysteresis. (English) Zbl 1276.35107

Summary: This 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.

MSC:

35K57 Reaction-diffusion equations
35K45 Initial value problems for second-order parabolic systems
47J40 Equations with nonlinear hysteresis operators
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