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Herrero, Miguel A. and 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

PDF
271kB |

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

## Abstract

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.

Item Type: | Book Section |
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Additional Information: | Proceedings of the IMA Workshop held at the University of Minnesota, Minneapolis, Minnesota, May 13–18, 1991 |

Uncontrolled Keywords: | Semilinear parabolic problems; blow up; asymptotic behaviour of solutions |

Subjects: | Sciences > Mathematics > Differential equations |

ID Code: | 22689 |

Deposited On: | 02 Sep 2013 13:46 |

Last Modified: | 02 Sep 2020 07:16 |

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