Advances in Difference Equations
Volume 2011 (2011), Article ID 925173, 25 pages
Research Article

Systems of Quasilinear Parabolic Equations with Discontinuous Coefficients and Continuous Delays

Department of Mathematics, Sichuan College of Education, Chengdu 610041, China

Received 24 December 2010; Accepted 3 March 2011

Academic Editor: Jin Liang

Copyright © 2011 Qi-Jian Tan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper is concerned with a weakly coupled system of quasilinear parabolic equations where the coefficients are allowed to be discontinuous and the reaction functions may depend on continuous delays. By the method of upper and lower solutions and the associated monotone iterations and by difference ratios method and various estimates, we obtained the existence and uniqueness of the global piecewise classical solutions under certain conditions including mixed quasimonotone property of reaction functions. Applications are given to three 2-species Volterra-Lotka models with discontinuous coefficients and continuous delays.