Global solvability of a mixed problem for a singular semilinear hyperbolic 1d system (Q6589473)

The authors investigate initial-boundary value problems for one-dimensional degenerate semilinear first-order hyperbolic systems coupled with nonlinear ODE systems. Such systems model physical processes with both finite and infinite propagation speed. The boundary conditions are nonlinear and nonlocal. All nonlinearities are assumed to be globally Lipschitz. By applying the Banach fixed-point theorem to an integral representation of the problem, the existence and uniqueness of global continuous solutions are established.