V. A. Kostin, D. V. Kostin, A. V. Kostin, “On the correct solvability of the Dirichlet boundary value problem for the generalized Helmholtz equation in a strip”, Dokl. RAN. Math. Inf. Proc. Upr., 2021, Volume 499,Pages <nobr>31

This article is cited in 1 paper

MATHEMATICS

On the correct solvability of the Dirichlet boundary value problem for the generalized Helmholtz equation in a strip

V. A. Kostin^a, D. V. Kostin^ab, A. V. Kostin^a

^a Voronezh State University, Voronezh, Russia
^b Voronezh State Pedagogical University, Voronezh, Russia

Abstract: Within the framework of the theory of operator cosine functions and its application, a solution of the Dirichlet boundary value problem for the generalized Helmholtz equation in a strip is found and the correct solvability of this problem is established. The critical width of the strip is found depending on the boundary conditions. Applying this result to the problem of heat propagation in a dihedral angle allows us to determine the angle of correctness of this problem and specify the law of heat propagation in the considered region.

Keywords: strongly continuous cosine functions and transformation semigroups, boundary value problems, correct solvability.

UDC: 517.9

Presented: V. P. Maslov
Received: 27.04.2021
Revised: 04.06.2021
Accepted: 15.06.2021

DOI: 10.31857/S2686954321040093