Existence of solution to Korteweg–de Vries equation in a non-parabolic domain

In this paper, we study the semilinear Korteweg–de Vries equation with time variable coefficients, subject to boundary conditions in a non-parabolic domain. Some assumptions on the boundary of the domain and on the coefficients of the equation will be imposed. The source term and its derivative with respect to t are taken in L2(Ω). The existence and uniqueness of the solution is obtained by using the parabolic regularization method, the Faedo–Galerkin and a method 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 Benia and Sadallah (2018).