Discontinuous reaction-diffusion equations under discontinuous and nonlocal flux conditions

In this paper, we consider a quasilinear parabolic equation with discontinu ous source term in a bounded cylindrical domain under nonlocal and disconti nuous flux conditions. Our main goal is to prove the existence of extremal solutions within a sector formed by appropriately defined upper and lower s olutions. The main tools used in the proof of our result are recently obtai ned abstract results on nonlinear evolution equations, an abstract fixed-po int result in partially ordered sets, compact embeddings, comparison, and t runcation techniques. (C) 2000 Elsevier Science Ltd. All rights reserved.