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phenomena may be related via a suitable change of dependent variables.

By Mr (k: K (k, Jong-shenq (rc-ntn) Souplet and Reviewed H. Marcinkowska


Fast rate of formation of dead-core for the heat equation with strong absorption and applications to fast blow-up. (English summary) Math. Ann. 331 (2005), no. 3, 651–667. The nonlinear heat equation ut = uxx − u p (t> 0, −1 < x < 1) equipped with the initial and boundary conditions u(t, ±1) = k (t> 0), u(0, x) = u0(x) (−1 < x < 1) is studied. The problem arises in the modelling of an isothermal reaction-diffusion process where the reactant, whose concentration is represented by u, is injected with a fixed concentration on the boundary. The number T = min{t> 0: m(t) = 0}, where m(t) = min u(t, x), |x|≤1 is called the dead-core time. The aim of the paper is to investigate the behavior of the function m(t) as t → T −. It is mentioned that according to the papers [C. Bandle and I. Stakgold, Trans

Year: 2013
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