We consider the class of boundary value problems for elliptic, parabolic, and hyperbolic equations in cylinders separated by a two-layer film into two half-cylinders. We prove the existence and uniqueness theorem and express the solutions in terms of solutions to analogous classical problems in cylinders without films.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D. A. Nomirovskii, “Generalized solvability of parabolic nonhomogeneous transmission conditions of nonideal contact type,” Differ. Equ. 40, No. 10, 1467–1477 (2004).
S. E. Kholodovskii, “On the solution of boundary value problems for the Laplace equation on the plane with a three-layer film inclusion,” Differ. Equ. 49, No. 12, 1655–1660 (2013).
S. E. Kholodovskii, “A method of convolution of Fourier expansions as applied to solving boundary value problems with intersecting interface lines,” Comput. Math. Math. Phys. 47, No. 9, 1489–1495 (2007).
A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics, Pergamon Press, Oxford etc. (1963).
S. E. Kholodovskii, “The convolution method of Fourier expansions. The case of a crack (screen) in an inhomogeneous space,” Differ. Equ. 45, No. 8, 1229-1233 (2009).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Sibirskii Zhurnal Chistoi i Prikladnoi Matematiki 16, No. 3, 2016, pp. 98-102.
Rights and permissions
About this article
Cite this article
Kholodovskii, S.E. Solution of Boundary Value Problems in Cylinders with Two-Layer Film Inclusions. J Math Sci 230, 55–59 (2018). https://doi.org/10.1007/s10958-018-3726-z
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-018-3726-z