A problem with a nonlocal, with respect to time, condition for multidimensional hyperbolic equations
Л. С. ПулькинаSamara National Research University named after Academician S. P. Korolyov, Moskovskoe sh. 34, Samara, 443086, RussiaА. Е. СавенковаSamara Technical State University, ul. Molodogvardeiskaya 244, Samara, 443100, Russia
2016en
ABI
Abstract
We study a boundary-value problem for a hyperbolic equation with a nonlocal with respect to time-variable integral condition. We obtain sufficient conditions for unique solvability of the nonlocal problem. The proof is based on reduction of the nonlocal first-type condition to the second-type one. This allows to reduce the nonlocal problem to an operator equation. We show that unique solvability of the operator equation implies the existence of a unique solution to the problem.
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Cited by 30 references