Bounded and almost periodic solvability of nonautonomous quasilinear hyperbolic systems

Abstract The paper concerns boundary value problems for general nonautonomous first-order quasilinear hyperbolic systems in a strip. We construct small global classical solutions, assuming that the right-hand sides are small. In case all data of problem almost periodic, we prove bounded solution is also periodic. For nonhomogeneous version linearized problem, provide stable dissipativity conditions ensuring unique continuous any smooth sides. autonomous case, this two times continuously differentiable. differentiable under additional conditions, which essential. A crucial ingredient our approach perturbation theorem linear systems. One technical complications overcome “loss smoothness” property PDEs.