Existence and uniqueness of solutions of system governed by second order quasilinear integro-partial differential equation of parabolic type

Abstract

Recently, Teo and Ahmed [17] have established the existence and uniqueness of solutions for a class of systems governed by second order quasilinear parabolic integro-partial differential equations. In their system equation, all but the second order coefficients are assumed to be bounded and measurable while more restrictive assumptions are imposed on the second order coefficients. In this paper, their results are generalized so that the second order coefficients can also be assumed to be bounded and measurable. However, the parabolic integro-partial differential equation is in “divergence form” and the solution of the system under consideration is in the sense of Aronson [1]. Our main result is presented in Theorem 3.6 which is proved using several fundamental results reported by Aronson [1].