Global smooth solutions of dissipative boundary value problems for first order quasilinear hyperbolic systems
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.
first order quasilinear hyperbolic systems
scientific article; zbMATH DE number 3935612