Similarity stabilizes blow-up

Steve Schochet

Journées équations aux dérivées partielles (1999)

  • page 1-7
  • ISSN: 0752-0360

Abstract

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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.

How to cite

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Schochet, Steve. "Similarity stabilizes blow-up." Journées équations aux dérivées partielles (1999): 1-7. <http://eudml.org/doc/93369>.

@article{Schochet1999,
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.},
author = {Schochet, Steve},
journal = {Journées équations aux dérivées partielles},
keywords = {similarity transformation; nonlocal equation; energy methods; time and location of blow-up},
language = {eng},
pages = {1-7},
publisher = {Université de Nantes},
title = {Similarity stabilizes blow-up},
url = {http://eudml.org/doc/93369},
year = {1999},
}

TY - JOUR
AU - Schochet, Steve
TI - Similarity stabilizes blow-up
JO - Journées équations aux dérivées partielles
PY - 1999
PB - Université de Nantes
SP - 1
EP - 7
AB - 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.
LA - eng
KW - similarity transformation; nonlocal equation; energy methods; time and location of blow-up
UR - http://eudml.org/doc/93369
ER -

References

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  1. [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. Zbl0851.35057MR97e:35077
  2. [CDE] C. Cortázar, M. Del Pino, and M. Elgueta : On the blow-up set for ut = ∆um + um, m &gt; 1, Indiana U. Math. J., Vol 47, (1998), p. 541-561. Zbl0916.35056MR99h:35085
  3. [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. Zbl0854.35033MR97d:35053
  4. [LR] D. Levy and P. Rosenau : On a class of thermal blow-up patterns, Physics Letters A, Vol. 236, (1997), p. 483-493. Zbl0969.35520MR1489695
  5. [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). Zbl1020.35001MR96b:35003
  6. [S] S. Schochet : Similarity stabilizes blow-up in quasilinear parabolic equations with balanced nonlinearity, in preparation. Zbl1004.35062

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