Short-wave asymptotics of solutions of the Cauchy problem for hyperbolic systems with constant coefficients and with characteristics of variable multiplicity

2014 ◽  
Vol 50 (5) ◽  
pp. 667-676
Author(s):  
I. N. Shchitov
Keyword(s):  
Cauchy Problem ◽  
Hyperbolic Systems ◽  
Short Wave ◽  
Asymptotics Of Solutions ◽  
Variable Multiplicity ◽  
The Cauchy Problem ◽  
Constant Coefficients

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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