On the Solvability of a Quasilinear Parabolic Problem with Neumann Boundary Condition - Aala, Mylen L.; Jose, Editha C.; Roque, Marian P. (Science Diliman: A Journal of Pure and Applied Sciences, 2016)
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