Global smooth solutions of dissipative boundary value problems for first order quasilinear hyperbolic systems. (English) Zbl 0584.35068
The author considers initial-boundary value problems for first order quasilinear hyperbolic systems and discusses the existence of global smooth solutions and the exponential decay of the solutions in \(C^ 1\)- space. Assuming a condition which is almost equivalent to the strict hyperbolicity, he gets a system of ordinary differential equations obtained along characteristic curves. Here he puts a condition on the boundary conditions which expresses the dissipative effect on the boundary, i.e., which guarantees the existence of global solutions for the above system of ordinary differential equations. Using this result, he obtains the global smooth solutions of the hyperbolic systems.
Reviewer: M.Tsuji
MSC:
35L50 | Initial-boundary value problems for first-order hyperbolic systems |
35L45 | Initial value problems for first-order hyperbolic systems |
35B40 | Asymptotic behavior of solutions to PDEs |
35B65 | Smoothness and regularity of solutions to PDEs |