Abstract:
In this paper we study a cross-diffusion system whose coefficient matrix is non-symmetric and degenerate. The system arises in the study of tissue growth with autophagy. The existence of a weak solution is established. We also investigate the limiting behavior of solutions as the pressure gets stiff. The so-called incompressible limit is a free boundary problem of Hele-Shaw type. Our key new discovery is that the usual energy estimate still holds as long as the time variable stays away from 0.
Duke University * Arts & Sciences * Physics * Faculty * Staff * Grad * Researchers * Reload * Login
Copyright (c) 2001-2002 by Duke University Physics.