On a class of nonlinear hyperbolic systems with nonlocal boundary conditions (Q5933406)

The author investigates an initial boundary-value problem for a semilinear hyperbolic system. This problem is written, using some operators, as a time-dependent Cauchy problem in some Hilbert space \(X\). The operator generated by the problem is proved to be a maximal monotone operator on \(X\). Based on nonlinear semigroup theory the author establishes existence and uniqueness of a strong solution to the problem under consideration.