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A. Lunardi (2003)
Analytic Semigroups and Optimal Regularity in Parabolic Problems
- Publisher
- Springer Journals
- Copyright
- Copyright © 2001 by Birkhäuser Verlag Basel,
- Subject
- Mathematics; Analysis
- ISSN
- 1424-3199
- DOI
- 10.1007/PL00001366
- Publisher site
- See Article on Publisher Site
Abstract
We study the stability of the planar travelling wave solution to a free boundary problem for the heat equation in the whole $ \Bbb R^2 $ . We turn the problem into a fully nonlinear parabolic system and establish a stability result which is the proper generalization of the one-dimensional case. The curvature terms contribute a gradient squared corresponding to critical growth. The latter is eliminated by means of the Hopf-Cole transformation.
Journal
Journal of Evolution Equations – Springer Journals
Published: Mar 1, 2001