A nonlocal problem for a hyperbolic equation with integral conditions of the 1st kind with time-dependent kernels

V. A. Steklov, “The Problem of Cooling of an Inhomogeneous Solid Rod,” Soobshch. Kharkovsk. Matem. Ob-va 5(3–4), 136–181 (1896).

V. B. Dmitriev, “Nonlocal Problem with Integral Conditions for theWave Equation,” Vestn. Samarsk. Univ. 2(42), 15–27 (2006).

N. L. Lazhetich, “On the Classical Solvability of the Mixed Problem for a Second-Order One-Dimensional Hyperbolic Equation,” Differents. Uravn. 42(8), 1072–1077 (2006).

A. I. Kozhanov, “On the Solvability of Spatially Nonlocal Boundary-Value Problems for Linear Parabolic Equations,” Vestn. Samarsk. Univ. 3(62), 165–174 (2008).

L.S. Pul’kina and A. V. Dyuzheva, “A Nonlocal Problem with Time-Dependent Steklov Boundary Conditions for a Hyperbolic Equation,” Vestn. Samarsk. Univ. 4(78), 56–64 (2010).

A. I. Kozhanov and L. S. Pul’kina, “About Solvability of Some Boundary Value Problems with Shifting for the Linear Hyperbolic Equations,” Matem. Zhurn. 9(2) (32), 78–92 (2009).

L. S. Pul’kina, “Boundary Value Problems for a Hyperbolic Equation with Nonlocal Conditions of the I and II Kind,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 4, 74–83 (2012) [Russian Mathematics (Iz. VUZ) 56 (4), 62–69 (2012)].

O. A. Ladyzhenskaya, The Boundary-Value Problems of Mathematical Physics (Nauka, Moscow, 1973) [in Russian].

L. K. Evans, Partial Differential Equations (Providence: AMS, 1998; Novosibirsk, 2003).