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

Mylen L. Aala, Editha C. Jose, Marian P. Roque


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

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