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.

Characterization of the dissipative structure for the symmetric hyperbolic system with non-symmetric relaxation

2021 ◽  
Vol 18 (01) ◽  
pp. 195-219
Author(s):  
Yoshihiro Ueda
Keyword(s):  
Hyperbolic System ◽  
Stability Condition ◽  
Dissipative Structure ◽  
General System ◽  
Partial Result ◽  
Symmetric Hyperbolic System ◽  
Standard Type ◽  
Classical Stability ◽  
The Stability

This paper is concerned with the dissipative structure for the linear symmetric hyperbolic system with non-symmetric relaxation. If the relaxation matrix of the system has symmetric property, Shizuta and Kawashima in 1985 introduced the suitable stability condition called Classical Stability Condition in this paper, and Umeda, Kawashima and Shizuta in 1984 analyzed the dissipative structure of the standard type. On the other hand, Ueda, Duan and Kawashima in 2012 and 2018 focused on the system with non-symmetric relaxation, and got the partial result which is the extension of known results. Furthermore, they argued the new dissipative structure called the regularity-loss type. In this situation, our purpose of this paper is to extend the stability theory introduced by Shizuta and Kawashima in 1985 and Umeda, Kawashima and Shizuta in 1984 for our general system.

scholarly journals Обобщенная задача Римана о распаде разрыва с дополнительными условиями на границе и ее применение для построения вычислительных алгоритмов

2019 ◽  
Vol 170 ◽  
pp. 38-50
Author(s):  
Юрий Иванович Скалько ◽  
Yu I Skalko ◽  
Сергей Юрьевич Гриднев ◽  
S Yu Gridnev
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Hyperbolic System ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Linear Differential Equations ◽  
Algebraic Equations ◽  
Order Linear ◽  
First Order ◽  
Linear Differential

We construct an approximation of the fundamental solution of a problem for a hyperbolic system of first-order linear differential equations with constant coefficients. We propose an algorithm for an approximate solution of the generalized Riemann problem on the breakup of a discontinuity under additional conditions at the boundaries, which allows one to reduce the problem of finding the values of variables on both sides of the discontinuity surface of the initial data to the solution of a system of algebraic equations. We construct a computational algorithm for an approximate solution of the initial-boundary-value problem for a hyperbolic system of first-order linear differential equations. The algorithm is implemented for a system of equations of elastic dynamics; it is used for solving some applied problems associated with oil production.

Quasiunitriangular groups

1993 ◽  
Vol 58 (1) ◽  
pp. 205-218 ◽  
Author(s):  
O. V. Belegradek
Keyword(s):  
Direct Summand ◽  
Algebraic Characterization ◽  
First Order ◽  
Expanded Group ◽  
The Matrix ◽  
Image Position

For a ring with unit R, which need not be associative, denote the group of upper unitriangular 3 × 3 matrices over R by UT3(R). Let e1 = (1,0,0), e2 = (0,1,0), where (α, β, γ) denotes the matrixDenote the expanded group (UT3(R), e1, e2) by (R). A. 1. Mal′cev [M] gave an algebraic characterization of the expanded groups of the form (R) as follows. Let h1, h2 be elements of a group H; then (H, h1, h2) is isomorphic to (R), for some R, if and only if(i) H is 2-step nilpotent;(ii) CH(hi) are abelian, i = 1,2;(iii) CH(h1) ∩ CH(h2) = Z(H);(iv) [CH(h1),h2] = [h1, CH(h2)] = Z(H);(v) Z(H) is a direct summand in both CH(hi).(In [M] condition (v) is a bit stronger; the version above is presented in [B2].)A pair (h1, h2) of elements of a group H is said to be a base if (H, h1, h2) satisfies the conditions (i)–(iv). A. I. Mal′cev [M] found a uniform way of first order interpreting a ring Ring(H, h1, h2) in any group with a base (H, h1, h2); in particular, Ring((R)) ≃ R.

An Algebraic Characterization of Concurrent Systems1

1988 ◽  
Vol 11 (2) ◽  
pp. 171-193
Author(s):  
Waldemar Korczyński
Keyword(s):  
Special Kind ◽  
Concurrent Systems ◽  
Algebraic Characterization ◽  
First Order ◽  
Order Language

In the paper a characterization of concurrent systems as algebras of a special kind is given. The algebras are defined by semi-equations in the first order language.

scholarly journals ALGEBRAIC CHARACTERIZATION OF LOGICALLY DEFINED TREE LANGUAGES

2010 ◽  
Vol 20 (02) ◽  
pp. 195-239 ◽  
Author(s):  
ZOLTÁN ÉSIK ◽  
PASCAL WEIL
Keyword(s):  
Algebraic Structure ◽  
Algebraic Characterization ◽  
Tree Language ◽  
Regular Tree ◽  
First Order ◽  
Product Operation ◽  
Finite Word ◽  
Tree Languages ◽  
Block Product

We give an algebraic characterization of the tree languages that are defined by logical formulas using certain Lindström quantifiers. An important instance of our result concerns first-order definable tree languages. Our characterization relies on the usage of preclones, an algebraic structure introduced by the authors in a previous paper, and of the block product operation on preclones. Our results generalize analogous results on finite word languages, but it must be noted that, as they stand, they do not yield an algorithm to decide whether a given regular tree language is first-order definable.

The asymptotic characteristic initial value problem for Einstein’s vacuum field equations as an initial value problem for a first-order quasilinear symmetric hyperbolic system

1981 ◽  
Vol 378 (1774) ◽  
pp. 401-421 ◽  
Keyword(s):  
Hyperbolic System ◽  
Initial Value Problem ◽  
Vacuum Field ◽  
Symmetric Hyperbolic System ◽  
Field Equations ◽  
Initial Value ◽  
Null Infinity ◽  
First Order ◽  
Asymptotic Characteristic ◽  
Characteristic Initial Value Problem

The asymptotic characteristic initial value problem for Einstein’s vacuum field equations where data are given on an incoming null hypersurface and on part of past null infinity is reduced to a characteristic initial value problem for a first-order quasilinear symmetric hyperbolic system of differential equations for which existence and uniqueness of solutions can be shown. It is delineated how the same method can be applied to the standard Cauchy problems for Einstein’s vacuum and conformal vacuum equations.

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