The Cauchy Problem for General Hyperbolic Systems in the Complete Scale of Sobolev Type Spaces

1999 ◽  
pp. 183-191
Author(s):  
Yakov Roitberg
Keyword(s):  
Cauchy Problem ◽  
Hyperbolic Systems ◽  
Sobolev Type ◽  
The Cauchy Problem ◽  
Sobolev Type Spaces ◽  
Type Spaces

scholarly journals Approximate solutions of equations defined by complex spherical multiplier operators

2005 ◽  
Vol 2005 (2) ◽  
pp. 93-115
Author(s):  
C. P. Oliveira
Keyword(s):  
Approximate Solutions ◽  
Positive Definite ◽  
Positive Definite Functions ◽  
Sobolev Type ◽  
Sobolev Type Spaces ◽  
Type Spaces ◽  
Solutions Of Equations ◽  
Multiplier Operators

This paper studies, in a partial but concise manner, approximate solutions of equations defined by complex spherical multiplier operators. The approximations are from native spaces embedded in Sobolev-type spaces and derived from the use of positive definite functions to perform spherical interpolation.

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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