Yassine Benia, Boubaker-Khaled Sadallah
This work is concerned with Burgers equation (with Dirichlet boundary conditions) in the non rectangular domain (where for all ). This domain will be transformed into a rectangle by a regular change of variables. The right-hand side lies in the Lebesgue space , and the initial condition is in the usual Sobolev space . Our goal is to establish the existence, uniqueness and the optimal regularity of the solution in the anisotropic Sobolev space.
Submitted April 15, 2016. Published June 21, 2016.
Math Subject Classifications: 35K58, 35Q35.
Key Words: Semilinear parabolic problem; Burgers equation; existence; uniqueness; anisotropic Sobolev space.
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| Yassine Benia |
Department of Mathematics
University of Tiaret, B.P. 78
14000, Tiaret, Algeria
| Boubaker-Khaled Sadallah |
Lab. PDE and Hist Maths
Dept of Mathematics, E.N.S.
16050, Kouba, Algiers, Algeria
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