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Título:
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Classification of blow-up with nonlinear diffusion and localized reaction
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Autores:
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Ferreira de Pablo, Raúl ;
Pablo, Arturo de ;
Vázquez, Juan Luis
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Tipo de documento:
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texto impreso
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Editorial:
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Elsevier, 2006-12-01
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Dimensiones:
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application/pdf
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Nota general:
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info:eu-repo/semantics/openAccess
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Idiomas:
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Palabras clave:
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Estado = Publicado
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Materia = Ciencias: Matemáticas: Ecuaciones diferenciales
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Tipo = Artículo
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Resumen:
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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)up where p > 0 and a(x) ? 0 is a compactly supported function. We investigate the existence and behaviour of the solutions of this problem in dependence of the exponents m and p. We prove that the critical exponent for global existence is p0 = (m + 1)/2, while the Fujita exponent is pc = m + 1: if 0 pc both global in time solutions and blowing up solutions exist. In the case of blow-up, we find the blow-up rates, the blow-up sets and the blow-up profiles; we also show that reaction happens as in the case of reaction extended to the whole line if p > m, while it concentrates to a point in the form of a nonlinear flux if p
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En línea:
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https://eprints.ucm.es/id/eprint/12493/1/2006classification-13.pdf
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