报告题目：Stability issues in some problems with free interface(s)
报告人：Claude-Michel Brauner , School of Mathematical Sciences ,Xiamen University
and Institut de Mathematiques de Bordeaux, Universite de Bordeaux
时间：2017年4月19日上午9:00―10：00
地点：管理科研楼1518教室
摘要：Two-dimensional propagating fronts with a free interface (or free boundary) have long been studied, in particular in combustion theory, where the unknown interface stands for the (thin) ame front. In the classical thermo-diusive model, the temperature gradient is discontinuous at the interface, hence the so-called /combustion type" free boundary conditions. In general, these problems admit a planar, one-dimensional, traveling wave solution, whose asymptotic
stability with respect to transverse perturbations is the issue at stake.In more recent years, propagating fronts with free interface have also been considered by several authors in problems with Stefan-like free boundary conditions. Models with two free interfaces have recently emerged, which request the extension of previous works for a single front.The talk will be divided in two parts: First, I will recall the method of [1] which allows the elimination of the free boundary in a class of overdetermined parabolic problems, at the expense of fully nonlinear terms. Second, I will describe a two-interface problem in a combustion model with ignition emperature (thick ame) and discuss the extension of the method. The main issue is that one of the interfaces does not satisfy the non-degeneracy condition of [1].
[1] C.-M. B., J. Hulshof and A. Lunardi, A general approach to the stability of Free Boundary Problems, J. Di. Eqns. 164(2000), p.16-48.1
stability with respect to transverse perturbations is the issue at stake.In more recent years, propagating fronts with free interface have also been considered by several authors in problems with Stefan-like free boundary conditions. Models with two free interfaces have recently emerged, which request the extension of previous works for a single front.The talk will be divided in two parts: First, I will recall the method of [1] which allows the elimination of the free boundary in a class of overdetermined parabolic problems, at the expense of fully nonlinear terms. Second, I will describe a two-interface problem in a combustion model with ignition emperature (thick ame) and discuss the extension of the method. The main issue is that one of the interfaces does not satisfy the non-degeneracy condition of [1].
[1] C.-M. B., J. Hulshof and A. Lunardi, A general approach to the stability of Free Boundary Problems, J. Di. Eqns. 164(2000), p.16-48.1
欢迎广大师生参加！