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Some results on blow up for semilinear parabolic problems

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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

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


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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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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:12 Dec 2018 15:08

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