### Anisotropic nonlinear diffusion with absorption: Existence and extinction.

Lair, Alan V., Oxley, Mark E. (1996)

International Journal of Mathematics and Mathematical Sciences

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Lair, Alan V., Oxley, Mark E. (1996)

International Journal of Mathematics and Mathematical Sciences

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International Journal of Mathematics and Mathematical Sciences

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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...

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