Geodesic
On the correct solvability of the Dirichlet boundary value problem for the generalized Helmholtz equation in a strip
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 499 (2021), pp. 31-34

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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. 
@article{DANMA_2021_499_a6,
     author = {V. A. Kostin and D. V. Kostin and A. V. Kostin},
     title = {On the correct solvability of the {Dirichlet} boundary value problem for the generalized {Helmholtz} equation in a strip},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {31--34},
     publisher = {mathdoc},
     volume = {499},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2021_499_a6/}
}
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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. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 499 (2021), pp. 31-34. http://geodesic.mathdoc.fr/item/DANMA_2021_499_a6/