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Velázquez, J.J. L. and Galaktionov, V. A. and Posashkov, S. A. and Herrero, Miguel A.
(1993)
*On a general approach to extinction and blow-up for quasi-linear heat equations.*
Computational Mathematics and Mathematical Physics, 33
(2).
pp. 217-227.
ISSN 0965-5425

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Official URL: http://www.mathnet.ru/links/d7d26db03f5293989ec731fcacfa35d5/zvmmf2764.pdf

## Abstract

The authors study asymptotic behaviour of positive solutions of equations of the type ut =Δφ(u)±Q(u), where φ′ and Q are given positive functions. By determining an auxiliary function F(u) appearing in an expression posed by A. Friedman and B. McLeod, they obtain asymptotic estimates of solutions as t→T, blow-up or extinction time. These estimates have been established by other authors using different methods. Moreover, the paper poses a conjecture that, if the behaviour of u(0,t) as t→T near a blow-up or extinction point is known, all the information about the corresponding asymptotic expansions on small compact subsets near the origin is encoded in the first order ODE φ′(u)ur+rF(u)=0 for r>0 as t→T, where an optimal choice of F(u) is indicated in the paper.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Friedman-McLeod method; blow-up; extinction; point; heat equation |

Subjects: | Sciences > Mathematics > Differential equations |

ID Code: | 18007 |

Deposited On: | 29 Jan 2013 09:44 |

Last Modified: | 19 Feb 2019 13:08 |

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