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Generic blow-up behavior of solutions of one-dimensional semilinear parabolic problems

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Herrero, Miguel A. and Velázquez, J.J. L. (1992) Generic blow-up behavior of solutions of one-dimensional semilinear parabolic problems. Comptes Rendus de l'Académie des Sciences. Série I. Mathématique , 314 (3). pp. 201-203. ISSN 0764-4442



Abstract

We consider the Cauchy problem (1) u(t) = u(xx) + u(p); x Є R, t > 0, p > 1 (2) u(x, 0) = u0 (x), x Є R, where u0(x) is continuous, nonnegative and bounded. Assume that the solution u(x, t) of (1), (2) blows up at x = 0, t = T. We describe here the generic asymptotic behaviour of u(x, t) as (x, t) approaches (0, T).


Item Type:Article
Uncontrolled Keywords:Blow-up; asymptotic behaviour; Cauchy problem; semilinear parabolic problems
Subjects:Sciences > Mathematics > Differential equations
ID Code:18049
Deposited On:30 Jan 2013 09:51
Last Modified:12 Dec 2018 15:08

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