scholarly journals Properties of the averaging along the characteristics hyperbolic of the system operator

2012 ◽  
Vol 53 ◽  
Author(s):  
Aleksandras Krylovas ◽  
Olga Lavcel-Budko
Keyword(s):  
Hyperbolic System ◽  
Initial Conditions ◽  
Riemann Invariants ◽  
Averaged Equations ◽  
System Operator ◽  
Linear Hyperbolic System

Examing the averaged equations system with periodic initial conditions. Proved the lemmas, which allow to reorganize the system in to the form similar to a semi-linear hyperbolic system written in Riemann invariants. This allows to set conditions for the existence of the solution.

Riesz basis of exponential family for a hyperbolic system

2019 ◽  
Vol 25 (1) ◽  
pp. 13-23
Author(s):  
Abdelkader Intissar ◽  
Aref Jeribi ◽  
Ines Walha
Keyword(s):  
Hilbert Space ◽  
Linear System ◽  
Hyperbolic System ◽  
Riesz Basis ◽  
Infinitesimal Generator ◽  
Exponential Family ◽  
Analysis Method ◽  
Spectral Analysis Method ◽  
Weaker Conditions ◽  
Linear Hyperbolic System

Abstract This paper studies a linear hyperbolic system with boundary conditions that was first studied under some weaker conditions in [8, 11]. Problems on the expansion of a semigroup and a criterion for being a Riesz basis are discussed in the present paper. It is shown that the associated linear system is the infinitesimal generator of a {C_{0}} -semigroup; its spectrum consists of zeros of a sine-type function, and its exponential system {\{e^{\lambda_{n}t}\}_{n\geq 1}} constitutes a Riesz basis in {L^{2}[0,T]} . Furthermore, by the spectral analysis method, it is also shown that the linear system has a sequence of eigenvectors, which form a Riesz basis in Hilbert space, and hence the spectrum-determined growth condition is deduced.

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