Abstract
In the present paper, the finite-difference method for the initial-boundary value problem for a hyperbolic system of equations with nonlocal boundary conditions is studied. The positivity of the difference analogy of the space operator generated by this problem in the space C with maximum norm is established. The structure of the interpolation spaces generated by this difference operator is investigated. The positivity of this difference operator in Hölder spaces is established. In applications, stability estimates for the solution of the difference scheme for a hyperbolic system of equations with nonlocal boundary conditions are obtained. A numerical example is applied. MSC:35L40, 35L45.
Highlights
Nonlocal problems are widely used for mathematical modeling of various processes of physics, ecology, chemistry, and industry, when it is impossible to determine the boundary or initial values of the unknown function
The method of operators as a tool for the investigation of the solution of local and nonlocal problems for partial differential equations in Hilbert and Banach spaces has been systematically developed by several authors
We introduce the Banach space C([, T]τ, E) of all continuous abstract mesh vector functions uτ =
Summary
Nonlocal problems are widely used for mathematical modeling of various processes of physics, ecology, chemistry, and industry, when it is impossible to determine the boundary or initial values of the unknown function. Stability estimates for the solution of the problem ( ) for the hyperbolic system of equations with nonlocal boundary conditions were obtained. The finite-difference method for the initial value problem for the hyperbolic system of equations with nonlocal boundary conditions is applied. The structure interpolation spaces generated by this difference operator is studied The positivity of this difference operator in Hölder spaces is established. In Section , the Green’s matrix function of the difference space operator is presented and positivity of this operator in the difference analogy of C[ , l] spaces is proved. In Section , the structure of fractional spaces generated by this difference operator is investigated and positivity of this difference operator in Hölder spaces is established.
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