The hyperbolic system of equations with nonlocal boundary conditions

Abstract

The initial value problem for the hyperbolic system of equations with nonlocal boundary conditions is studied. The positivity of the space operator A generated by this problem in interpolation spaces is established. The structure interpolation spaces of this state operator is studied. The positivity of this space operator in Hölder spaces is established. In applications, the stability estimates for the hyperbolic system of equations with nonlocal boundary conditions are obtained.