Uniqueness and stability of solutions for a type of parabolic boundary value problem
We consider a boundary value problem consisting of the one-dimensional parabolic equation \(gu_ t=(hu_ x)_ x+q\), 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 for the equation, we prove the uniqueness of a nonnegative solution that depends continuously on boundary values.
scientific article; zbMATH DE number 4148706