 A singular boundary value problem for evolution equations of hyperbolic typeAnar T. Assanova and Roza E. Uteshova Chaos, Solitons & Fractals, 2021, vol. 143, issue C Abstract: This paper deals with a problem of finding a bounded in a strip solution to a system of second order hyperbolic evolution equations, where the matrix coefficient of the spatial derivative tends to zero as t→∓∞. The problem is studied under assumption that the coefficients, the right-hand side of the system, and the boundary function belong to some spaces of functions continuous and bounded with a weight. By introducing new unknown functions, the problem in question is reduced to an equivalent problem consisting of singular boundary value problems for a family of first order ordinary differential equations and some integral relations. Existence conditions are established for a bounded in a strip solutions to a family of ordinary differential equations, whose matrix tends to zero as t→∓∞ and the right-hand side is bounded with a weight. Conditions for the existence of a unique solution to the original problem are obtained. Keywords: System of evolution equations of hyperbolic type; Bounded in a strip solution; Singular boundary value problem; Family of ordinary differential equations; Non-uniform partition; Method of parametrization; Solvability (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:143:y:2021:i:c:s0960077920309097 DOI: 10.1016/j.chaos.2020.110517 Access Statistics for this article Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros More articles in Chaos, Solitons & Fractals from Elsevier |
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