Displaying similar documents to “A necessary and sufficient condition for global existence for a quasilinear reaction-diffusion system.”

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...

Weak solutions of a parabolic-elliptic type system for image inpainting

Zhengmeng Jin, Xiaoping Yang (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we consider the initial boundary value problem of a parabolic-elliptic system for image inpainting, and establish the existence and uniqueness of weak solutions to the system in dimension two.