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Some results on blow up for semilinear parabolic problems

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Herrero, Miguel A. y Velázquez, J.J. L. (1993) Some results on blow up for semilinear parabolic problems. In Degenerate diffusions. IMA Volumes in Mathematics and its Applications (47). Springer, New York, pp. 105-125. ISBN 0-387-94068-5

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URL Oficial: http://link.springer.com/chapter/10.1007%2F978-1-4612-0885-3_7


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The authors describe the asymptotic behavior of blow-up for the semilinear heat equation ut=uxx+f(u) in R×(0,T), with initial data u0(x)>0 in R, where f(u)=up, p>1, or f(u)=eu. A complete description of the types of blow-up patterns and of the corresponding blow-up final-time profiles is given. In the rescaled variables, both are governed by the structure of the Hermite polynomials H2m(y). The H2-behavior is shown to be stable and generic. The existence of H4-behavior is proved. A nontrivial blow-up pattern with a blow-up set of nonzero measure is constructed. Similar results for the absorption equation ut=uxx−up, 0<p<1, are discussed.


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Proceedings of the IMA Workshop held at the University of Minnesota, Minneapolis, Minnesota, May 13–18, 1991

Palabras clave:Semilinear parabolic problems; blow up; asymptotic behaviour of solutions
Materias:Ciencias > Matemáticas > Ecuaciones diferenciales
Código ID:22689
Depositado:02 Sep 2013 13:46
Última Modificación:28 Nov 2013 17:51

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