Global Solvability in the Whole Space for a Class of First Order Quasilinear Hyperbolic Systems

摘要

The global solvability in the whole (t,x) space is considered for first-order quasilinear hyperbolic systems; the conditions satisfied by the system itself in order that the system admit global smooth solutions in the whole (t,x) space (GSSWS) are determined. In order to get the existence of a nontrivial (unknown functions not equal to constants) GSSWS, the system of equations involved does not have to be linearly degenerate. This is proved for general quasilinear systems of diagonal form with n equations. Finally, the case of non-strictly hyperbolic systems is considered briefly. (Atomindex citation 14:751905)