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We study the asymptotic behaviour of nonnegative solutions of the nonlinear diffusion equation in the half-line with a nonlinear boundary condition, ut = uxx ? _(u + 1) logp(u + 1) (x, t) € R+ × (0, T),?ux(0, t) = (u + 1) logq(u + 1)(0, t) t € ([...]texto impreso
We study the behaviour of nonnegative solutions of the reaction-diffusion equation _ ut = (um)xx + a(x)up in R × (0, T), u(x, 0) = u0(x) in R. The model contains a porous medium diffusion term with exponent m > 1, and a localized reaction a(x)u[...]texto impreso
Arrieta Algarra, José María ; Ferreira de Pablo, Raúl ; Pablo, Arturo de ; Rossi, Julio D. | American Institute of Mathematical Sciences | 2010In this paper we prove a general result concerning continuity of the blow-up time and the blow-up set for an evolution problem under perturbations. This result is based on some convergence of the perturbations for times smaller than the blow-up [...]
