On the retention of the interfaces in some elliptic and parabolic nonlinear problems
Luis Álvarez, Jesús Ildefonso Díaz Díaz · Discrete and Continuous Dynamical Systems · 2009
We study some retention phenomena on the free boundaries associatedto some elliptic and parabolic problems of reaction-diffusion type. This isthe case, for instance, of the waiting time phenomenon for solutionsof suitable parabolic equations. We find sufficient conditions in order tohave a discrete version of the waiting time property (the so callednondiffusion of the support) for solutions of the associated familyof elliptic equations and prove how to pass to the limit in order to get thisproperty for the solutions of the parabolic equation.