Galerkin Method for First-Order Hyperbolic Systems with Two Independent Variables - Lavrenyuk, S. P.; Oliskevych, M. O. (Ukrains’kyi Matematychnyi Zhurnal, 2002)
We investigate a mixed problem for a weakly nonlinear first-order hyperbolic system with two independent variables in bounded and unbounded domains. Assuming that the nonlinearities are monotonic, we obtain conditions for the existence and uniqueness of a generalized solution; these conditions do not depend on the behavior of a solution as x → +∞.