International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 4, Pages 735-739

Uniqueness and stability of solutions for a type of parabolic boundary value problem

Enrique A. Gonzalez-Velasco

Department of Mathematics, University of Lowell, Lowell, Massachusetts, USA

Received 25 June 1986; Revised 10 October 1986

Copyright © 1989 Enrique A. Gonzalez-Velasco. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider a boundary value problem consisting of the one-dimensional parabolic equation gut=(hux)x+q, where g, h and q are functions of x, subject to some general boundary conditions. By developing a maximum principle for the boundary value problem, rather than the equation, we prove the uniqueness of a nonnegative solution that depends continuously on boundary values.