On the Solvability of a Quasilinear Parabolic Problem with Neumann Boundary Condition

Abstract

This paper establishes the existence and uniquenesss of a weak solution of a quasilinear parabolic problem in an open set whose boundary is the union of two disjoint closed surfaces. A Dirichlet condition is prescribed on the exterior boundary and a Neumann condition on the interior boundary. The existence of a solution of the parabolic problem is shown using the Faedo-Galerkin method and some a priori estimates are established to provide bounds for the solution.

Keywords

• Parabolic
• quasilinear
• Neumann boundary condition
• weak solution