Arendt, Wolfgang; Chill, Ralph Global existence for quasilinear diffusion equations in isotropic nondivergence form. (English) Zbl 1223.35202 Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 9, No. 3, 523-539 (2010). The authors consider a quasilinear parabolic equation. By using the maximal regularity of a nonautonomous linear parabolic equation in the energy space, they are able to apply Schaefer’s fixed point theorem and prove global existence of a solution. Their result can be applied in several contexts. Reviewer: Vincenzo Vespri (Firenze) Cited in 11 Documents MSC: 35K59 Quasilinear parabolic equations 35A01 Existence problems for PDEs: global existence, local existence, non-existence 35K10 Second-order parabolic equations Keywords:maximal regularity; Schaefer’s fixed point theorem PDFBibTeX XMLCite \textit{W. Arendt} and \textit{R. Chill}, Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 9, No. 3, 523--539 (2010; Zbl 1223.35202) Full Text: DOI