A non-local problem with integral conditions of the first kind for the string vibration equation

Abstract

The article considers a problem with integral nonlocal conditions of the first kind. The main goal is to prove the unique solvability of a nonlocal problem with integral conditions of the 1st kind, if the kernels of these conditions depend not only on the spatial variable, but also on time. The equivalence of a nonlocal problem with integral conditions of the 1st kind and a nonlocal problem with integral conditions of the 2nd kind is shown. Restrictions on the input data are obtained to ensure the uniqueness of a generalized solution to the problem posed.

Keywords

• hyperbolic equation
• nonlocal problem
• integral conditions
• generalized solution