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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].

35K65Parabolic equations of degenerate type
35K60Nonlinear initial value problems for linear parabolic equations
45K05Integro-partial differential equations
35B05Oscillation, zeros of solutions, mean value theorems, etc. (PDE)