Cauchy Problem for Quasilinear Hyperbolic Systems with Higher Order Dissipative Terms

2003 ◽  
Vol 19 (1) ◽  
pp. 71-82 ◽  
Author(s):  
Wei-guo Zhang
Keyword(s):  
Cauchy Problem ◽  
Hyperbolic Systems ◽  
Higher Order ◽  
Quasilinear Hyperbolic Systems ◽  
Dissipative Terms

Global smooth solutions for a class of quasilinear hyperbolic systems with dissipative terms

1997 ◽  
Vol 127 (6) ◽  
pp. 1311-1324 ◽  
Author(s):  
Tong Yang ◽  
Changjiang Zhu ◽  
Huijiang Zhao
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Existence Theorem ◽  
Hyperbolic Systems ◽  
A Priori ◽  
Smooth Solutions ◽  
Quasilinear Hyperbolic Systems ◽  
Global Smooth Solutions ◽  
The Cauchy Problem ◽  
Dissipative Terms

In this paper we prove an existence theorem of global smooth solutions for the Cauchy problem of a class of quasilinear hyperbolic systems with nonlinear dissipative terms under the assumption that only the C0-norm of the initial data is sufficiently small, while the C1-norm of the initial data can be large. The analysis is based on a priori estimates, which are obtained by a generalised Lax transformation.

Singularities of solutions for first order quasilinear hyperbolic systems

1983 ◽  
Vol 94 (1-2) ◽  
pp. 137-147 ◽  
Author(s):  
Lee Da-tsin(Li Ta-tsien) ◽  
Shi Jia-hong
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Hyperbolic Systems ◽  
Smooth Solutions ◽  
Small Initial Data ◽  
Quasilinear Hyperbolic Systems ◽  
First Order ◽  
Global Smooth Solutions ◽  
The Cauchy Problem

SynopsisIn this paper, the existence of global smooth solutions and the formation of singularities of solutions for strictly hyperbolic systems with general eigenvalues are discussed for the Cauchy problem with essentially periodic small initial data or nonperiodic initial data. A result of Klainerman and Majda is thus extended to the general case.

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