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Global existence in some reaction-diffusion systems. (English) Zbl 0595.35053

Summary: We present two different technics to show the existence of solutions for all time in some reaction-diffusion systems for which classical methods fail. One is based on a duality argument coupled with \(L^ p\)-regularity results for the linear heat equation; then \(L^{\infty}\)-bounds are derived. The second one is based on \(L^ 1\)-technics and exploit the a priori \(L^ 1\)-estimate provided by the preservation of total mass.

MSC:

35K05 Heat equation
35B65 Smoothness and regularity of solutions to PDEs
35B35 Stability in context of PDEs
35A15 Variational methods applied to PDEs
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