Existence of solutions to Burgers equations in a non-parabolic domain

Abstract

In this article, we study the semilinear Burgers equation with time variable coefficients, subject to boundary condition in a non-parabolic domain. Some assumptions on the boundary of the domain and on the coefficients of the equation will be imposed. The right-hand side of the equation is taken in L2(Ω). The method we used is based on the approximation of the non-parabolic domain by a sequence of subdomains which can be transformed into regular domains. This paper is an extension of the work [2].