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Uniqueness of transverse solutions for reaction-diffusion equations with spatially distributed hysteresis. (English) Zbl 1252.35009
Summary: The paper deals with reaction-diffusion equations involving a hysteretic discontinuity in the source term, which is defined at each spatial point. Such problems describe biological processes and chemical reactions in which diffusive and nondiffusive substances interact according to the hysteresis law. Under the assumption that the initial data is spatially transverse, we prove a theorem on the uniqueness of solutions. The theorem covers the case of non-Lipschitz hysteresis branches arising in the theory of slow-fast systems.

MSC:
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
35K57 Reaction-diffusion equations
35K45 Initial value problems for second-order parabolic systems
47J40 Equations with nonlinear hysteresis operators
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