Journal
MATHEMATICAL AND COMPUTER MODELLING
Volume 32, Issue 11-13, Pages 1333-1344Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/S0895-7177(00)00208-9
Keywords
quasilinear parabolic equations; discontinuous nonlinearities; nonlocal and discontinuous boundary conditions; upper and lower solutions; pseudomonotone operators; truncation and comparison techniques; extremal solutions
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In this paper, we consider a quasilinear parabolic equation with discontinuous source term in a bounded cylindrical domain under nonlocal and discontinuous flux conditions. Our main goal is to prove the existence of extremal solutions within a sector formed by appropriately defined upper and lower solutions. The main tools used in the proof of our result are recently obtained abstract results on nonlinear evolution equations, an abstract fixed-point result in partially ordered sets, compact embeddings, comparison, and truncation techniques. (C) 2000 Elsevier Science Ltd. All rights reserved.
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