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

Enrique A. Gonzalez-Velasco
1989 International Journal of Mathematics and Mathematical Sciences  
We consider a boundary value problem consisting of the one-dimensional parabolic equationgut=(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.
doi:10.1155/s0161171289000918 fatcat:cgmmvfuf5vgc3c6lhw4qbhm4dy