Messaoudi, Salim A. Blow-up of solutions of a semilinear heat equation with a visco-elastic term. (English) Zbl 1088.35030 Chipot, Michel (ed.) et al., Nonlinear elliptic and parabolic problems. A special tribute to the work of Herbert Amann, Zürich, Switzerland, June 28–30, 2004. Basel: Birkhäuser (ISBN 3-7643-7266-4/hbk). Progress in Nonlinear Differential Equations and their Applications 64, 351-356 (2005). Summary: We consider an initial boundary value problem related to the equation \[ u_t-\Delta u+\int^t_0g(t-s)\Delta u(x,s)ds=|u|^{p-2}u \] and prove, under suitable conditions on \(g\) and \(p\), a blow-up result for solutions with negative or vanishing initial energy. This result improves an earlier one by the author.For the entire collection see [Zbl 1077.00009]. Cited in 1 ReviewCited in 16 Documents MSC: 35K65 Degenerate parabolic equations 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations 45K05 Integro-partial differential equations 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs Keywords:relaxation function; negative initial energy; vanishing initial energy PDFBibTeX XMLCite \textit{S. A. Messaoudi}, Prog. Nonlinear Differ. Equ. Appl. 64, 351--356 (2005; Zbl 1088.35030)