Skip to main content

Systems of Quasilinear Parabolic Equations with Discontinuous Coefficients and Continuous Delays

Abstract

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.

Publisher note

To access the full article, please see PDF.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Qi-Jian Tan.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Tan, QJ. Systems of Quasilinear Parabolic Equations with Discontinuous Coefficients and Continuous Delays. Adv Differ Equ 2011, 925173 (2011). https://doi.org/10.1155/2011/925173

Download citation

Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Functional Equation