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On Solvability of Conjugation Problems with Non-Ideal Contact Conditions

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Abstract

In this paper, we study the regular solvability (in Sobolev spaces) of transmission problems for parabolic second-order systems with conjugation conditions of non-ideal contact type. The solution of such a problem has all generalized derivatives entering in the equation that are summable with some power \(p\in (1,\infty)\). One can express limit values of conormal derivatives at the interface in terms of combinations of limit values of the solution. This problem, arising when describing heat and mass transfer processes, differs from the classical statement of diffraction problems. The proof relies on derived a priori estimates and on the method of continuation in a parameter.

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Funding

This work was supported by the Russian Foundation for Basic Research (grant 18-01-00620a) and grant no. 13-01-20/43 for the development of scientific schools of the Ugra State University in priority research areas.

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Authors and Affiliations

  1. Yugra State University, 16 Chekhov str., 628012, Khanty-Mansiysk, Russia

    V. A. Belonogov & S. G. Pyatkov

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  1. V. A. Belonogov
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  2. S. G. Pyatkov
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Correspondence to V. A. Belonogov or S. G. Pyatkov.

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Russian Text © The Author(s), 2019, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, No. 7, pp. 18–32.

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Belonogov, V.A., Pyatkov, S.G. On Solvability of Conjugation Problems with Non-Ideal Contact Conditions. Russ Math. 64, 13–26 (2020). https://doi.org/10.3103/S1066369X20070038

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