The initial value problem for hyperbolic equationsHilbert space H is considered. The first and second order accuracy difference schemes generated by the integer power of A approximately solving this initial value problem are presented. The stability estimates for the solution of these difference schemes are obtained.

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Stability estimates for the solution of the nonlocal boundary value problem with two integral conditions for hyperbolic equations in a Hilbert space H are established. In applications, stability estimates for the solution of the nonlocal boundary value problems for hyperbolic equations are obtained. MSC: 35L10

Abstract. The boundary value problem of determining the parameter of an elliptic equationwith a positive operator A in an arbitrary Banach space E is studied. The exact estimates are obtained for the solution of this problem in Hölder norms. Coercive stability estimates for the solution of boundary value problems for multi-dimensional elliptic equations are established.

The Cauchy problem for abstract telegraph equations

In this paper, the initial value problem for the first order partial differential equation with the nonlocal boundary condition is studied. In applications, the stability estimates for the first order partial differential equation with the nonlocal boundary condition are obtained. The finite difference method for the initial value problem for hyperbolic equations with nonlocal boundary conditions is applied. In practice, the stability estimates for the solution of the difference scheme of the problem for hyperbolic equations with nonlocal boundary conditions are obtained.