Pierre, Michel Global existence in some reaction-diffusion systems. (English) Zbl 0595.35053 Delft Prog. Rep. 10, 283-289 (1985). 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. Cited in 1 Document MSC: 35K05 Heat equation 35B65 Smoothness and regularity of solutions to PDEs 35B35 Stability in context of PDEs 35A15 Variational methods applied to PDEs Keywords:reaction-diffusion systems; duality argument; \(L^ p\)-regularity; preservation of total mass PDFBibTeX XMLCite \textit{M. Pierre}, Delft Prog. Rep. 10, 283--289 (1985; Zbl 0595.35053)