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On behavior of solutions of the quasilinear second-order parabolic equations in unbounded noncylindrical domains

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Abstract

The theorems of uniqueness of solutions are formulated in the classes of increasing functions for a mixed initial boundary value problem for the second-order degenerate quasiparabolic equations in unbounded noncylindrical domains. We presenta priori estimates of a special kind, analogous to the Saint-Venant principle. The proofs are based on the method of introducing a parameter.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, Donetsk

    V. V. Kurta

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  1. V. V. Kurta
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Translated from Ukrainskii Matematicheskii Zhumal, Vol. 45, No. 4, pp. 492–499, April, 1993.

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Kurta, V.V. On behavior of solutions of the quasilinear second-order parabolic equations in unbounded noncylindrical domains. Ukr Math J 45, 526–534 (1993). https://doi.org/10.1007/BF01062949

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  • DOI: https://doi.org/10.1007/BF01062949

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