Nonlocal problems with integral conditions for hyperbolic equations with two time variables

G. A. Varlamova   ; A. I. Kozhanov

Matematičeskie zametki SVFU, Tome 30 (2023) no. 3, pp. 12-26

Résumé

The work is devoted to the study of solvability of boundary value problems with nonlocal conditions of integral form for the differential equations $$u_xt - au_xx + c(x, t)u = f(x, t)$$, in which $x \in \Omega = (0, 1), t \in (0, T), 0 < T < +\infty, a \in R$, and $c(x, t)$ and $f(x, t)$ are known functions. The peculiarity of these equations is that any of variables t and x can be considered a temporary variable, and in accordance with this, for these equations, formulations of boundary value problems with different carriers of boundary conditions can be proposed. For the problems under study, the work proves existence and uniqueness theorems for regular solutions; namely, solutions that have all derivatives generalized according to S. L. Sobolev and included in the equation.

Détail

Keywords: hyperbolic equation, nonlocal problem, integral condition, regular solution, uniqueness.
Mots-clés : existence