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Herrero, Miguel A. and Velázquez, J.J. L.
(1992)
*Generic behaviour of one-dimensional blow up patterns.*
Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV, 19
(3).
pp. 381-450.
ISSN 0391-173X

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Official URL: http://www.numdam.org/item?id=ASNSP_1992_4_19_3_381_0

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## Abstract

This paper concerns the Cauchy problem ut−uxx=up, x∈R, t>0, u(x,0)=u0(x), x∈R, where p>1 and u0(x) is a continuous, nonnegative and bounded function. It has been previously proved that if x=x¯, t=T is a blow-up point, then there are three cases for the asymptotic behavior of a solution near the blow-up point. The main result of this paper is to prove that if u0∈C+0(R), blow-up consists generically of a single point blow-up, with the behavior described in one case (case (b)). Moreover, the behavior is stable under small perturbations in the L∞-norm of the initial value u0.

Item Type: | Article |
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Uncontrolled Keywords: | Generic behaviour; blow up |

Subjects: | Sciences > Mathematics > Differential equations |

ID Code: | 22699 |

Deposited On: | 03 Sep 2013 14:24 |

Last Modified: | 12 Dec 2018 15:08 |

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