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
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
. 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
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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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