Geodesic
Uniqueness of the solution of the first mixed problem for a two-dimentional nonlinear parabolic equation
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIII, Tome 248 (1998), pp. 60-69

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The first mixed problem for two-dimentional nonlinear parabolic equation with nonlinear second derivatives of a desired function is considered. We assume that the solution possessing continuous second derivatives with respect to coordinate variables exists in a closed cylinder under some restrictions on initial data of the problem. The uniqueness of this problem is proved by using the longitudinal version of the method of lines. 
@article{ZNSL_1998_248_a3,
     author = {A. P. Kubanskaya},
     title = {Uniqueness of the solution of the first mixed problem for a two-dimentional nonlinear parabolic equation},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {60--69},
     publisher = {mathdoc},
     volume = {248},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1998_248_a3/}
}
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A. P. Kubanskaya. Uniqueness of the solution of the first mixed problem for a two-dimentional nonlinear parabolic equation. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIII, Tome 248 (1998), pp. 60-69. http://geodesic.mathdoc.fr/item/ZNSL_1998_248_a3/