Displaying similar documents to “Reaction diffusion equations and quadratic convergence.”

Systems of reaction-diffusion equations with spatially distributed hysteresis

Pavel Gurevich, Sergey Tikhomirov (2014)

Mathematica Bohemica

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We study systems of reaction-diffusion equations with discontinuous spatially distributed hysteresis on the right-hand side. The input of the hysteresis is given by a vector-valued function of space and time. Such systems describe hysteretic interaction of non-diffusive (bacteria, cells, etc.) and diffusive (nutrient, proteins, etc.) substances leading to formation of spatial patterns. We provide sufficient conditions under which the problem is well posed in spite of the assumed discontinuity...