A semilinear problem related to Burgers' equation. Issue 3 (11th February 2023)

• Record Type: Journal Article
• Authors: Benia, Yassine; Sadallah, Boubaker-Khaled
• Is Part Of: Applicable analysis. Volume 102:Issue 3(2023)
• Page Start: 938
• Page End: 957
• Publication Date: 2023-02-11
• Subjects: Semilinear parabolic equation -- Burgers equation -- existence -- uniqueness -- regularity -- anisotropic Sobolev space; 35K58 -- 35Q35; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2021.1967331
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : In this work, we study the existence, uniqueness and regularity of the solution to a semilinear Cauchy–Dirichlet problem with variable coefficients, using the Faedo–Galerkin method. We applied this study to a nonhomogeneous Burgers problem considered in a nonparabolic domain. We give a new regularity result of the solution in an anisotropic Sobolev space.