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

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

Published
2016-12-15
Issue
Vol 28 No 2 (2016)
Section
Articles
Submission of a manuscript implies: that the work described has not been published before (except in the form of an abstract or as part of a published lecture, review, or thesis); that it is not under consideration for publication elsewhere; that its publication has been approved by all co-authors, if any, as well as by the responsible authorities at the institute where the work has been carried out; that, if and when the manuscript is accepted for publication, the authors agree to the automatic transfer of the copyright to the publisher; that the manuscript will not be published elsewhere in any language without the consent of the copyright holders; that written permission of the copyright holder is obtained by the authors for material used from other copyrighted sources; and that any costs associated with obtaining this permission are the authors’ responsibility.