The behaviour of induced discontinuities behind a first order discontinuity wave for a quasi-linear hyperbolic system

1987 ◽  
Vol 38 (1) ◽  
pp. 65-78 ◽  
Author(s):  
Alessandra Borrelli ◽  
Maria Cristina Patria
Keyword(s):  
Hyperbolic System ◽  
First Order ◽  
Linear Hyperbolic System ◽  
Order Discontinuity

scholarly journals Characterization of Dissipative Structures for First-Order Symmetric Hyperbolic System with General Relaxation

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 728
Author(s):  
Yasunori Maekawa ◽  
Yoshihiro Ueda
Keyword(s):  
Hyperbolic System ◽  
Dissipative Structure ◽  
Dissipative Structures ◽  
Algebraic Characterization ◽  
Symmetric Hyperbolic System ◽  
Full Generality ◽  
Order Linear ◽  
First Order

In this paper, we study the dissipative structure of first-order linear symmetric hyperbolic system with general relaxation and provide the algebraic characterization for the uniform dissipativity up to order 1. Our result extends the classical Shizuta–Kawashima condition for the case of symmetric relaxation, with a full generality and optimality.

scholarly journals P- waves reflected from the "20" discontinuity" beneath the Mediterranean region

2010 ◽  
Vol 28 (1) ◽  
Author(s):  
A BOTTARI ◽  
B. FEDERICO
Keyword(s):  
Mediterranean Area ◽  
P Wave ◽  
Travel Times ◽  
P Waves ◽  
First Order ◽  
P Wave Velocity ◽  
Different Depths ◽  
The Mediterranean ◽  
Regional Character ◽  
Order Discontinuity

The observed travel-times of the P-waves for twenty shallow, intermediate, and deep earthquakes, with epicenters in the Mediterranean area, are used in order to analyze some characteristics of the upper mantle. A first- order discontinuity, identifiable as the "20° discontinuity", is found at a depth of 505 ± 16 km in the area underneath the Mediterranean basin. The velocity contrast is equal to 12% (above T'= 8.9 km/sec; below V= 9.97 km/sec). Assuming that this discontinuity gives rise to reflected P-waves (PdP), the travel times of these waves are calculated for various hypocentral depths. The observation of impulses identified as PdP on the seismograms of Messina supports this hypothesis. This result and its implications are discussed in the contest of the conclusions of various authors who locate a P-wave velocity-discontinuity at different depths between 400 and 580 km. Finally, particular emphasis is given to the regional character of the analyzed structures in question.

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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