Amann, Herbert Global existence for semilinear parabolic systems. (English) Zbl 0564.35060 J. Reine Angew. Math. 360, 47-83 (1985). This paper studies the problem of global existence for strongly coupled semilinear parabolic systems of arbitrary even order under linear time- dependent boundary conditions. In particular it is shown that there exist classical global solutions provided the nonlinearity satisfies appropriate polynomial growth restrictions and a priori estimates in some weak norm (e.g. \(L_ 1\)-estimates) are known. The methods are essentially functional analytical. Cited in 81 Documents MSC: 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations 35A05 General existence and uniqueness theorems (PDE) (MSC2000) 35K35 Initial-boundary value problems for higher-order parabolic equations 47J05 Equations involving nonlinear operators (general) Keywords:global existence; coupled semilinear parabolic systems; even order; time- dependent boundary conditions; a priori estimates PDFBibTeX XMLCite \textit{H. Amann}, J. Reine Angew. Math. 360, 47--83 (1985; Zbl 0564.35060) Full Text: DOI Crelle EuDML