Electron. J. Differential Equations, Vol. 2018 (2018), No. 20, pp. 1-13.

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

Yassine Benia, Boubaker-Khaled Sadallah

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 $L^2(\Omega)$. 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].

Submitted December 14, 2017. Published January 15, 2018.
Math Subject Classifications: 35K58, 35Q35.
Key Words: Burgers equation; existence; uniqueness; non-parabolic domains; anisotropic Sobolev space.

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Yassine Benia
Dept of Mathematics and Informatics
University of Benyoucef Benkhedda (Alger 1)
16000, Algiers, Algeria
email: benia.yacine@yahoo.fr
Boubaker-Khaled Sadallah
Lab. PDE & Hist Maths; Dept of Mathematics, E.N.S.
16050, Kouba, Algiers, Algeria
email: sadallah@ens-kouba.dz

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