A semilinear problem related to Burgers' equation

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.

Keywords:

• Semilinear parabolic equation
• Burgers equation
• existence
• uniqueness
• regularity
• anisotropic Sobolev space

Mathematics Subject Classifications (2010):

• 35K58
• 35Q35

Disclosure statement

No potential conflict of interest was reported by the authors.