Abstract
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 solutions is proved by applying the longitudinal version of the method of straight lines. Bibliography: 4 titles.
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References
A. P. Kubanskaya, “Method of straight lines in application to some two-dimensional nonlinear parabolic equations”,Zap. Nauchn. Semin. LOMI,159, 132–142 (1987).
S. M. Lozinskii, “Approximate methods for solving the Cauchy problem for a system of ordinary differential e equations”,Proc. of the Fourth All-Union Mathematical Congress, [in Russian], Vol. 2 (1964), pp. 606–613.
M. N. Yakovlev. “Estimating the approximate solution of the Cauchy problem”,Zap. Nauchn. Semin. LOMI,23, 140–142. (1971).
M. N. Yakovlev, “The method of straight lines in nonlinear boundary-value problems for nonlinear parabolic equations”,Zap. Nauchn. Semin. LOMI,23, 143–150 (1971).
Additional information
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 248, 1998, pp. 60–69.
Translated by N. S. Zabavnikova
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Kubanskaya, A.P. Uniqueness of the solution of the first mixed problem for a two-dimensional nonlinear parabolic equation. J Math Sci 101, 3261–3266 (2000). https://doi.org/10.1007/BF02672771
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DOI: https://doi.org/10.1007/BF02672771