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Characterization of blow-up for a semilinear heat equation with a convection term. (English) Zbl 0694.76035

Summary: We consider the convective semilinear heat equation \(u_ t=\Delta u+e^ u-| \nabla u|^ 2\) on bounded domains with analytic boundaries. Conditions for the existence of a blow-up point and finite blow-up time are given. A description of the asymptotic behaviour of the solution u(x,t) near the blow-up points is also given. Finally, a weak formulation of solutions is discussed which allows one to analyse post-blow-up phenomena.

MSC:

76R50 Diffusion
35Q99 Partial differential equations of mathematical physics and other areas of application
35L65 Hyperbolic conservation laws
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