# Similarity stabilizes blow-up

Journées équations aux dérivées partielles (1999)

- page 1-7
- ISSN: 0752-0360

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topSchochet, 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

top- [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
- [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. Zbl0916.35056MR99h:35085
- [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
- [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
- [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
- [S] S. Schochet : Similarity stabilizes blow-up in quasilinear parabolic equations with balanced nonlinearity, in preparation. Zbl1004.35062

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