Izv. Vyssh. Uchebn. Zaved. Mat., 2016, Number 10, Pages 41–52
This article is cited in 2 scientific papers (total in 2 papers)
A problem with a nonlocal with respect to time condition for multidimensional hyperbolic equations
L. S. Pul'kinaa, A. E. Savenkovab
a Samara National Research University named after academician S. P. Korolyov, 34 Moskovskoe Highway, Samara, 443086 Russia
b Samara Technical State University, 244 Molodogvardeiskaya str., Samara, 443100 Russia
We study the boundary-value problem for hyperbolic equation with nonlocal with respect to time-variable condition in integral form. We obtain sufficient conditions for the unique solvability of the nonlocal problem. The proof is based on possibility to reduce a nonlocal condition of the first kind to the second kind 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 posed problem.
hyperbolic equation, nonlocal problem, integral conditions, generalized solution.
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Russian Mathematics (Izvestiya VUZ. Matematika), 2016, 60:10, 33–43
L. S. Pul'kina, A. E. Savenkova, “A problem with a nonlocal with respect to time condition for multidimensional hyperbolic equations”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 10, 41–52; Russian Math. (Iz. VUZ), 60:10 (2016), 33–43
Citation in format AMSBIB
\by L.~S.~Pul'kina, A.~E.~Savenkova
\paper A~problem with a~nonlocal with respect to time condition for multidimensional hyperbolic equations
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\jour Russian Math. (Iz. VUZ)
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A. K. Urinov, Sh. T. Nishonova, “A Problem with Integral Conditions for an Elliptic-Parabolic Equation”, Math. Notes, 102:1 (2017), 68–80
S. Z. Dzhamalov, “The nonlocal boundary value problem with constant coefficients for the mixed type of equation of the first kind in a plane”, Malays. J. Math. Sci., 12:1 (2018), 49–62
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