Constantin, Adrian; Peszat, Szymon Global existence of solutions of semilinear parabolic evolution equations. (English) Zbl 1038.35025 Differ. Integral Equ. 13, No. 1-3, 99-114 (2000). The authors deal with the problem of the existence of a global solution to the following semilinear problem \[ \partial_tu+ Au=F(u),\;u(0)= u_0\tag{1} \] where \(A\) is the infinitesimal generator of a \(C_0\)-semigroup \(\{S(t)\}_{t\geq 0}\) on \(V\) and the nonlinear mapping \(F\) acts continuously from \(E\) into \(V\). Here \(E\) and \(V\) are \(B\)-spaces such that \(E\) is densely and continuously embedded into \(V\). They apply their abstract results to the heat equation with first order nonlinear perturbations, Cahn-Hilliard and Fitz Hugh-Nagumo systems. Reviewer: Messoud A. Efendiev (Berlin) Cited in 4 Documents MSC: 35K55 Nonlinear parabolic equations 35K15 Initial value problems for second-order parabolic equations 35K90 Abstract parabolic equations PDFBibTeX XMLCite \textit{A. Constantin} and \textit{S. Peszat}, Differ. Integral Equ. 13, No. 1--3, 99--114 (2000; Zbl 1038.35025)