Global Classical Solutions to the Mixed Initial-boundary Value Problem fora Class of Quasilinear Hyperbolic Systems of Balance Laws

[摘要] It is proven that the mixed initial-boundary value problem for a class of quasilinear hyperbolic systems of balancelaws with general nonlinear boundary conditions in the half space |{(t, x) | t 0, x 0} ≥ ≥ admits a unique global C1solution u u(t, x) = with small C1 norm, provided that each characteristic with positive velocity is weakly linearlydegenerate. This result is also applied to the flow equations of a model class of fluids with viscosity induced by fadingmemory.

[关键词] Mixed initial-boundary value problem;Global classicalsolution;Quasilinear hyperbolic;systems of balance laws;Weaklylinearly degenerate characteristics