The Existence and the Non-existence of Global Solutions of a Free Boundary Problem

Abstract

" We study a free boundary problem of parabolic equations with a positive parameter \u03c4 included in the coefficient of the derivative with respect to the time variable t. This problem arises from some reaction-diffusion system. We prove that, if \u03c4 is large enough, the solution exists for 0 < t < +\u221e while, if \u03c4 is small enough, the solution exists only in finite time."