Initial boundary value problem for one-dimensional hyperbolic compressible Navier-Stokes equations

Abstract: An initial boundary value problem for one-dimensional hyperbolic compressible Navier-Stokes equations is investigated. After transforming the system into Lagrangian coordinate, the resulting system possesses a structure with uniform characteristic boundary. By constructing an approximate system with non-characteristic boundary, we get a uniform global smooth solutions and obtain a global solution of the original problem by passing to a limit. Moreover, the global relaxation limit is also obtained.