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

  • Mylen L. Aala First Asia Institute of Technology and Humanities
  • Editha C. Jose University of the Philippines Los Baños
  • Marian P. Roque University of the Philippines Diliman


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