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
and prove, under suitable conditions on and , a blow-up result for solutions with negative or vanishing initial energy. This result improves an earlier one by the author.
|35K65||Parabolic equations of degenerate type|
|35K60||Nonlinear initial value problems for linear parabolic equations|
|45K05||Integro-partial differential equations|
|35B05||Oscillation, zeros of solutions, mean value theorems, etc. (PDE)|