scholarly journals A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty

2017 ◽  
Vol 345 ◽  
pp. 224-244 ◽  
Author(s):  
Kailiang Wu ◽  
Huazhong Tang ◽  
Dongbin Xiu
Keyword(s):  
Galerkin Method ◽  
Hyperbolic Systems ◽  
Quasilinear Hyperbolic Systems ◽  
First Order ◽  
Stochastic Galerkin Method ◽  
Stochastic Galerkin

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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