Existence of solution to Korteweg–de Vries equation in a non-parabolic domain. (June 2020)

• Record Type: Journal Article
• Authors: Benia, Yassine; Scapellato, Andrea
• Is Part Of: Nonlinear analysis. Volume 195(2020)
• Publication Date: 2020-06
• Subjects: 35K58 -- 35Q35; Anisotropic Sobolev space -- KdV equation -- Existence -- Uniqueness -- Non-parabolic domain; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2020.111758
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: 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 L 2 ( 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).