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oai:docta.ucm.es:20.500.14352/577482023-08-10T23:36:27Zcom_20.500.14352_14col_20.500.14352_15

Plane structures in thermal runaway Herrero, Miguel A. Velázquez, J.J. L. 517.9 536.2 Semilinear heat-equations point blow-up Ecuaciones diferenciales 1202.07 Ecuaciones en Diferencias We consider the problem (1) u(t) = u(xx) + e(u) when x is-an-element-of R, t > 0, (2) u (x, 0) = u0(x) when x is-an-element-of R, where u0(x) is continuous, nonnegative and bounded. Equation (1) appears as a limit case in the analysis of combustion of a one-dimensional solid fuel. It is known that solutions of (1), (2) blow-up in a finite time T, a phenomenon often referred to as thermal runaway. In this paper we prove the existence of blow-up profiles which are flatter than those previously observed. We also derive the asymptotic profile of u(x, T) near its blow-up points, which are shown to be isolated. CICYT Grant EEC Contract Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas TRUE pub 2023-06-20T17:05:16Z 2023-06-20T17:05:16Z 1993-10 journal article https://hdl.handle.net/20.500.14352/57748 0021-2172 10.1007/BF02764836 eng PB90-0235 SC1-0019-C restricted access application/pdf Hebrew University Magnes Press