scholarly journals The Cauchy problem for weakly hyperbolic systems

2017 ◽  
Vol 43 (1) ◽  
pp. 25-46
Author(s):  
F. Colombini ◽  
Guy Métivier
Keyword(s):  
Cauchy Problem ◽  
Hyperbolic Systems ◽  
The Cauchy Problem ◽  
Weakly Hyperbolic Systems

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.

scholarly journals On the Cauchy problem for microlocally symmetrizable hyperbolic systems with log-Lipschitz coefficients

2020 ◽  
Vol 69 (3) ◽  
pp. 785-836
Author(s):  
Ferruccio Colombini ◽  
Daniele Del Santo ◽  
Francesco Fanelli ◽  
Guy Métivier
Keyword(s):  
Cauchy Problem ◽  
Hyperbolic Systems ◽  
The Cauchy Problem
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