A singular boundary value problem for evolution equations of hyperbolic type
Assanova A.T. Uteshova R.E.
February 2021Elsevier Ltd
Chaos, Solitons and Fractals
2021#143
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.
Bounded in a strip solution , Family of ordinary differential equations , Method of parametrization , Non-uniform partition , Singular boundary value problem , Solvability , System of evolution equations of hyperbolic type
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Institute of Mathematics and Mathematical Modeling
International Information Technology University
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