Global Cauchy problems on Rn for weakly hyperbolic systems with coefficients admitting superlinear growth for |x| → ∞

2019 ◽  
Vol 150 ◽  
pp. 35-61
Author(s):  
Daniel Gourdin ◽  
Todor Gramchev
Keyword(s):  
Hyperbolic Systems ◽  
Cauchy Problems ◽  
Superlinear Growth ◽  
Weakly Hyperbolic Systems

Convergence of the viscosity method for some nonlinear hyperbolic systems

1994 ◽  
Vol 124 (2) ◽  
pp. 341-352 ◽  
Author(s):  
Yunguang Lu
Keyword(s):  
Perturbation Theory ◽  
Hyperbolic Systems ◽  
Artificial Viscosity ◽  
Singular Perturbation Theory ◽  
Compensated Compactness ◽  
Cauchy Problems ◽  
Single Variable ◽  
Viscosity Method ◽  
Entropy Flux ◽  
Nonlinear Hyperbolic Systems

In this paper some special entropy–entropy flux pairs of Lax type are constructed for nonlinear hyperbolic systems of types (1.1) and (1.2), in which the progression terms are functions of a single variable. The necessary estimates for the major terms are obtained by the use of singular perturbation theory. The special entropies provide a convergence theorem in the strong topology for the artificial viscosity method when applied to the Cauchy problems (1.1), (1.3) and (1.2), (1.3) and used together with the theory of compensated compactness.

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