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Computing Solutions of Symmetric Hyperbolic Systems of PDE's

Svetlana Selivanova, Victor Selivanov
2008 Electronical Notes in Theoretical Computer Science  
We study the computability properties of symmetric hyperbolic systems of PDE' . . . , xm). Such systems first considered by K.O.  ...  ϕ ∈ C k+1 (Q, R n ), k ≥ 1, to the unique solution u ∈ C k (H, R n ), where Q = [0, 1] m and H is the nonempty domain of correctness of the system.  ...  Acknowledgement We are grateful to Vasco Brattka for sending us some preprints on computability in linear algebra and to Vadim Isaev for some useful hints concerning approximations.  ... 
doi:10.1016/j.entcs.2008.12.021 fatcat:6gwss5oyprdmznjdm6sieyleve

Foreword

Matthew Witten
1985 Computers and Mathematics with Applications  
Lakshmlkantham and Pandlt address the question of penodlc solutions of hyperbolic pde's Bloom examines systems of nonlinear hyperbolic pde's which anse m problems of classical electromagnetic theory Bellman  ...  hyperbolic pde's Layton discusses the long time behavior of finite difference and finite element approximations to first order hyperbolic systems Begue and Plronneau address the question of hyperbolic  ... 
doi:10.1016/0898-1221(85)90133-6 fatcat:2fh7hh3j5fanbjyac7jpxsn3dq

The Spin-2 Equation on Minkowski Background [chapter]

Florian Beyer, George Doulis, Jörg Frauendiener, Ben Whale
2013 Progress in Mathematical Relativity, Gravitation and Cosmology  
The linearised general conformal field equations in their first and second order form are used to study the behaviour of the spin-2 zero-rest-mass equation on Minkowski background in the vicinity of space-like  ...  a system of first order PDE's.  ...  Equations (1), when appropriately combined, split into three constraint equations and a symmetric hyperbolic (in the domain |t| < κ −1 ) system of five evolution equations, see [1] .  ... 
doi:10.1007/978-3-642-40157-2_71 fatcat:zmwyhihso5chjozxfeks7hzrwu

Book Review: Differential operators for partial differential equations and function theoretic applications

Peter A. McCoy
1983 Bulletin of the American Mathematical Society  
Its solutions arise in the Maxwell system for modelling electric or magnetic «-poles, in potential scattering and as the initial data for parabolic PDE's.  ...  Since then it has grown to encompass PDE's of elliptic, parabolic and hyperbolic types into an active field of research referred to as "Function Theoretic Methods in Partial Differential Equations".  ...  Several of these group theorists are presently working hard to decrease the size of the proof.  ... 
doi:10.1090/s0273-0979-1983-15220-5 fatcat:6c5d6zprtrghzcwraknaycn3py

Numerical methods for the hydrodynamic device model: subsonic flow

C.L. Gardner, J.W. Jerome, D.J. Rose
1989 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems  
Arguments for existence of solutions and convergence of numerical methods are given for the case of subsonic electron flow.  ...  Special attention is paid to classifying the hydrodynamic PDE's and analyzing their nonlinear wave structure.  ...  AV, compute the new solution, etc.  ... 
doi:10.1109/43.24878 fatcat:ilq6lzxg2jhfrojcamefzgeniu

Page 2414 of Mathematical Reviews Vol. , Issue 2001D [page]

2001 Mathematical Reviews  
Joachim (D-AACH-NM; Aachen); Lorenz, Jens (1-NM-MS; Albuquerque, NM) Hyperbolic systems with relaxation: symmetrizers and entropies.  ...  The author obtains estimates on the decay rate of solutions as time goes to infinity for a class of semilinear hyperbolic systems, including Maxwell’s equations for the propagation of electromag- netic  ... 

Page 7812 of Mathematical Reviews Vol. , Issue 2003j [page]

2003 Mathematical Reviews  
Comput. 24 (2002), no. 2, 480-506 (electronic). The authors present a fourth-order central weighted non- oscillatory (WENO) scheme for two-dimensional hyperbolic systems of conservation laws.  ...  But in the case of nonlinear hyperbolic systems of conservation laws, the speed of propagation at a point is not unique and shocks may appear.  ... 

On Behavior Of Preconditioned Methods For A Class Of Compact Finite Difference Schemes In Solution Of Hyperbolic Equations

A. Golbabai, M.m. Arabshahi
2011 Journal of Mathematics and Computer Science  
Numerical results performed on model problem to confirm the efficiency of our approach.  ...  in solution of hyperbolic equations ) u , u u, t, F(x, t)u (x, -u 1-Introduction: When solving PDE's by means of numerical methods one often has to deal with large systems of linear equations, especially  ...  applied for non-symmetric systems.  ... 
doi:10.22436/jmcs.03.01.03 fatcat:i5xpsopcojcuhi67kpcnwwmjj4

Strongly Hyperbolic Extensions of the ADM Hamiltonian [chapter]

J. David Brown
2009 Quantum Mechanics of Fundamental Systems: The Quest for Beauty and Simplicity  
The ADM Hamiltonian formulation of general relativity with prescribed lapse and shift is a weakly hyperbolic system of partial differential equations.  ...  In general weakly hyperbolic systems are not mathematically well posed.  ...  I especially thank Olivier Sarbach for his patient explanations of hyperbolicity. This work was supported by NSF Grant PHY-0600402.  ... 
doi:10.1007/978-0-387-87499-9_6 fatcat:d7afvzo4tfgu5kstr4zf77nliu

Partial Differential Equations in the 20th Century

Haıïm Brezis, Felix Browder
1998 Advances in Mathematics  
Computation of solutions of PDE 's: Numerical analysis and computational science.  ...  Models of PDE 's in the 18th and 19th century. 3. Methods of calculating solutions in the 19th century. 4. Developments of rigorous theories of solvability in the last decades of the 19th century. 5.  ...  Friedrichs on symmetric hyperbolic systems, the full generality of the pre-war results of Petrovski [Pet] was recovered and amplified by J. Leray [Le4] using global energy estimates.  ... 
doi:10.1006/aima.1997.1713 fatcat:w5r6fnew4feplacukxf57kdw3u

Page 7783 of Mathematical Reviews Vol. , Issue 97M [page]

1997 Mathematical Reviews  
The author describes essentially non-oscillatory finite-volume methods for the numerical solution of hyperbolic conservation laws.  ...  These matrices are sparse, banded and symmetric, and are therefore convenient for computer application.” 97m:65183 65M60 65M55 Schoombie, S. W. (SA-OFS-AM; Bloemfontein) ; Mare, E.  ... 

Page 596 of Mathematical Reviews Vol. , Issue 2002A [page]

2002 Mathematical Reviews  
In this paper, we take a hyperbolic system of conservation laws as a governing system of equations for reacting gases and propose an algorithm to deter- mine a wave propagation speed uniquely.  ...  [Robertson, Mairi] (4-STRA; Glasgow A moving mesh finite element method for the solution of two-dimensional Stefan problems. (English summary) J. Comput. Phys. 168 (2001), no. 2, 500-518.  ... 

Optimal LQ-feedback control for a class of first-order hyperbolic distributed parameter systems

Ilyasse Aksikas, Joseph J. Winkin, Denis Dochain
2008 E S A I M: Control, Optimisation and Calculus of Variations  
Next the LQ-feedback operator is computed by using the corresponding operator Riccati algebraic equation whose solution is obtained via a related matrix Riccati differential equation in the space variable  ...  The Linear-Quadratic (LQ) optimal control problem is studied for a class of first-order hyperbolic partial differential equation models by using a nonlinear infinite-dimensional (distributed parameter)  ...  The work of the first author has been partially carried out within the framework of a collaboration agreement between CESAME (Université Catholique de Louvain, Belgium) and LINMA of the Faculty of Sciences  ... 
doi:10.1051/cocv:2008015 fatcat:h6ma5auuprehfemmslpkagc6xq

List of papers presented at the congress

1996 Journal of Computational and Applied Mathematics  
Schott, On the computation of polynomial representations of nilpotent Lie groups: a symbolic mathematical approach K. Frishmuth, Numerical solution to a hyperbolic heat transfer model G.N.  ...  Bar-On, Parallel computation of the eigenvalues and eigenvectors of very large size tridiagonal and band symmetric matrices * D. Bessis, Pad~ approximations in noise filtering I. Bin Mohd, A.B.  ...  Redivo-Zaglia, Acceleration with prediction in the solution of uniformly accurate schemes for hyperbolic systems M.-T. Noda and H.  ... 
doi:10.1016/0377-0427(96)90021-7 fatcat:rg2odu6vzrgq3bwqttmsz7g4da

Exponential Stability and Transfer Functions of Processes Governed by Symmetric Hyperbolic Systems

Cheng-Zhong Xu, Gauthier Sallet
2002 E S A I M: Control, Optimisation and Calculus of Variations  
Using the theory of symmetric hyperbolic systems, we prove exponential stability of the underlying semigroup for the heat exchanger network.  ...  Our results remain valid for a wide class of processes governed by symmetric hyperbolic systems. Mathematics Subject Classification. 93D09, 93D25, 80A20, 35L50.  ...  As pointed out in Ydstie and Alonso [42] , many thermodynamic processes satisfying a system of conservation laws are governed in particular by symmetric hyperbolic systems of PDE's.  ... 
doi:10.1051/cocv:2002062 fatcat:6uw42kxkgbgxpnlpvzr2ruiiva
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