Systems of Quasilinear Parabolic Equations with Discontinuous Coefficients and Continuous Delays

[摘要] 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.

[学科分类] 数学（综合）

[关键词] Differential Equation;Partial Differential Equation;Ordinary Differential Equation;Functional Analysis;Functional Equation