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.
Highlights
Reaction-diffusion equations with time delays have been studied by many researchers see 1–8 and references therein
All of the discussions in the literature are devoted to the equations with continuous coefficients
We prove the lemma by the principle of induction
Summary
Reaction-diffusion equations with time delays have been studied by many researchers see 1–8 and references therein. We consider a weakly coupled system of quasilinear parabolic equations where the coefficients are allowed to be discontinuous and the reaction functions may depend on continuous infinite or finite delays.
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