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  • Journées équations aux dérivées partielles
  • Year 1999
  • article no. 12
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Similarity stabilizes blow-up
Steve Schochet
Journées équations aux dérivées partielles (1999), article no. 12, 7 p.
  • Abstract

The blow-up of solutions to a quasilinear heat equation is studied using a similarity transformation that turns the equation into a nonlocal equation whose steady solutions are stable. This allows energy methods to be used, instead of the comparison principles used previously. Among the questions discussed are the time and location of blow-up of perturbations of the steady blow-up profile.

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EuDML: 93369 | MR: 1718994 | Zbl: 01810585
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@article{JEDP_1999____A12_0,
     author = {Steve Schochet},
     title = {Similarity stabilizes blow-up},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {12},
     publisher = {Universit\'e de Nantes},
     year = {1999},
     mrnumber = {1718994},
     zbl = {01810585},
     language = {en},
     url = {https://proceedings.centre-mersenne.org/item/JEDP_1999____A12_0/}
}
TY  - JOUR
AU  - Steve Schochet
TI  - Similarity stabilizes blow-up
JO  - Journées équations aux dérivées partielles
PY  - 1999
PB  - Université de Nantes
UR  - https://proceedings.centre-mersenne.org/item/JEDP_1999____A12_0/
LA  - en
ID  - JEDP_1999____A12_0
ER  - 
%0 Journal Article
%A Steve Schochet
%T Similarity stabilizes blow-up
%J Journées équations aux dérivées partielles
%D 1999
%I Université de Nantes
%U https://proceedings.centre-mersenne.org/item/JEDP_1999____A12_0/
%G en
%F JEDP_1999____A12_0
Steve Schochet. Similarity stabilizes blow-up. Journées équations aux dérivées partielles (1999), article  no. 12, 7 p. https://proceedings.centre-mersenne.org/item/JEDP_1999____A12_0/
  • References
  • Cited by

[BG] J. Bebernes and V. A. Galaktionov : On classification of blow-up patterns for a quasilinear heat equation, Differential and Integrals Eqs., Vol 9, (1996), p. 655-670. | MR | Zbl

[CDE] C. Cortázar, M. Del Pino, and M. Elgueta : On the blow-up set for ut = ∆um + um, m > 1, Indiana U. Math. J., Vol 47, (1998), p. 541-561. | MR | Zbl

[CEF] C. Cortázar, M. Elgueta, and P. Felmer : Symmetry in an elliptic problem and the blow-up set of a quasilinear heat equation, Commun. Partial Differential Equations, Vol. 21, (1996), p.507-520. | MR | Zbl

[LR] D. Levy and P. Rosenau : On a class of thermal blow-up patterns, Physics Letters A, Vol. 236, (1997), p. 483-493. | MR | Zbl

[SGKM] A.A Samarskii, V. A. Galaktionov, S. P. Kurdyumov, and A. P. Mikhailov : Blow-up in Quasilinear Parabolic Equations, Walter de Gruyter, Berlin (1995). | MR | Zbl

[S] S. Schochet : Similarity stabilizes blow-up in quasilinear parabolic equations with balanced nonlinearity, in preparation.

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