@Article{JPDE-19-48,
author = {Xinfu Chen  and Congyu Gao },
title = {Well-posedness of a Free Boundary Problem in the Limit of Slow-diffusion Fast-reaction Systems},
journal = {Journal of Partial Differential Equations},
year = {2006},
volume = {19},
number = {1},
pages = {48--79},
abstract = {<p>We consider a free boundary problem obtained from the asymptotic limit of a FitzHugh-Nagumo system, or more precisely, a slow-diffusion, fast-reaction equation governing a phase indicator, coupled with an ordinary differential equation governing a control variable ν. In the range (-1, 1), the v value controls the speed of the propagation of phase boundaries (interfaces) and in the mean time changes with dynamics depending on the phases. A new feature included in our formulation and thus made our model different from most of the contemporary ones is the nucleation phenomenon: a phase switch occurs whenever v elevates to 1 or drops to -1. For this free boundary problem, we provide a weak formulation which allows the propagation, annihilation, and nucleation of interfaces, and excludes interfaces from having (space- time) interior points. We study, in the one space dimension setting, the existence, uniqueness, and non-uniqueness of weak solutions. A few illustrating examples are also included.</p>},
issn = {2079-732X},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jpde/5320.html}
}