Uniqueness of the solution of the first mixed problem for a two-dimensional nonlinear parabolic equation

The first mixed problem for a two-dimensional nonlinear parabolic equation with nonlinear occurrences of the second derivatives of the unknown function is considered. Under the assumption that a solution possessing continuous second derivatives with respect to the coordinate variables exists in a closed cylinder and under certain constraints on the initial data of the problem, the uniqueness of this solution is proved by applying the longitudinal version of the method of straight lines. ©2000 Kluwer Academic/Plenum Publishers.