Abstract
One of directions in the development of Lomov’s regularization method is the approach related to holomorphic regularization of singularly perturbed problems, which allows one to construct solutions to such problems in the form of series in powers of a small parameter that converge in the usual sense. For boundary-value problems, the problem of pseudo-holomorphic continuation of solutions is very urgent. In this paper, we examine a boundary-value problem for a Tikhonov system and give conditions for the existence of its pseudo-holomorphic solution.
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 172, Proceedings of the Voronezh Winter Mathematical School “Modern Methods of Function Theory and Related Problems,” Voronezh, January 28 – February 2, 2019. Part 3, 2019.
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Kachalov, V.I. Holomorphic Regularization of Boundary-Value Problems for Tikhonov Systems. J Math Sci 268, 63–69 (2022). https://doi.org/10.1007/s10958-022-06180-5
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DOI: https://doi.org/10.1007/s10958-022-06180-5
Keywords and phrases
- holomorphic regularization
- pseudo-holomorphic solution
- Tikhonov system
- pseudo-holomorphic continuation
- essentially singular manifold