The global existence of a parabolic cross-diffusion system with discontinuous coefficients

摘要

This paper deals with a one-dimensional parabolic cross-diffusion system describing two-species models. The system under consideration is strongly coupled and the coefficients of the equations are allowed to be discontinuous. The existence and uniqueness of nonnegative global solutions are given when one of the cross-diffusion pressures is zero. Our approach to the problem is by an approximation method and various estimates.