Journal
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Volume 44, Issue 3, Pages 1674-1693Publisher
SIAM PUBLICATIONS
DOI: 10.1137/110848839
Keywords
reaction-diffusion; cross diffusion; quasilinear systems; global existence; population dynamics
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We prove global existence in time of solutions to relaxed conservative cross diffusion systems governed by nonlinear operators of the form u(i) -> partial derivative(t)u(i) - Delta(a(i)((u) over bar )u(i)), where the u(i), i = 1, ... , I, represent I density functions, (u) over bar is a spatially regularized form of (u(1), ... , u(I)), and the nonlinearities a(i) are merely assumed to be continuous and bounded from below. Existence of global weak solutions is obtained in any space dimension. Solutions are proved to be regular and unique when the a(i) are locally Lipschitz continuous.
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