Stability in a two-dimensional free boundary combustion model

✍ Scribed by Luca Lorenzi; Alessandra Lunardi

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 497 KB
• Volume: 53
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(02)00289-4

✦ Synopsis

We prove rigorously the stability of the planar travelling wave solution to a free boundary system in R 2 , arising as a model in combustion theory, for appropriate values of the reduced Lewis number. After changements of coordinates and unknowns, the problem is reduced to the stability of the null solution of a ÿxed boundary parabolic system. The di culties consist in the fact that the ÿnal system is fully nonlinear, and the spectrum of the linearized system contains the hal ine (-∞; 0]. They are overcome setting the problem in a suitably weighted H older space.