International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 4, Pages 735-739
doi:10.1155/S0161171289000918

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

Abstract

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.