Search

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.

In this paper, we discuss the n-dimensional diffraction problem for weakly coupled quasilinear parabolic system on a bounded domain Ω, where the interfaces ( ) are allowed to intersect with the outer boundary ∂ Ω and the coefficients of the equations are allowed to be discontinuous on the interfaces. The aim is to show the existence of solutions by approximation method. The approximation problem is a diffraction problem with interfaces, which do not intersect with ∂ Ω. MSC:35R05, 35K57, 35K65.