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Systems of partial differential equations reflecting conservation laws hold significant relevance to a variety of theoretical and practical applications, including compressible fluid flow, electromagnetism, elasticity theory, and other areas of continuum mechanics. This field of nonlinear analysis is currently experiencing a marked increase in successful research activity.
The EU-TMR network "Hyperbolic Systems of Conservation Laws held a summer program offering short courses on the Analysis of Systems of Conservation Laws. This book contains five of the self-contained short courses presented during this program by experts of international reputation. These courses, which address solutions to hyperbolic systems by the front tracking method, non-strictly hyperbolic conservation laws, hyperbolic-elliptic coupled systems, hyperbolic relaxation problems, the stability of nonlinear waves in viscous media and numerics, and more, represent the state of the art of most central aspects of the field.
| Preface | |
| Analysis of solutions to hyperbolic systems by the front tracking method | p. 1 |
| A wave-front tracking algorithm | p. 3 |
| Continuous dependence on initial data | p. 16 |
| A front tracking algorithm for 2 x 2 systems | p. 27 |
| Uniqueness of the Standard Riemann Semigroup | p. 34 |
| Characterization of semigroup trajectories | p. 37 |
| Unique solutions to the Cauchy problem | p. 43 |
| Hyperbolic conservation laws: Global solutions to systems with umbilic degeneracy and initial boundary value problems in L[infinity] | p. 49 |
| Global solutions to systems with umbilic degeneracy | p. 50 |
| Initial boundary value problems in L[infinity] | p. 64 |
| The initial value problem for hyperbolic-elliptic coupled systems and applications to radiation hydrodynamics | p. 87 |
| Introduction | p. 87 |
| Entropy function and symmetrization | p. 89 |
| Local existence | p. 94 |
| Stability condition | p. 99 |
| Global existence | p. 102 |
| Proof of a priori estimate | p. 104 |
| Decay properties for the linearized system | p. 108 |
| Decay estimate | p. 111 |
| Large-time approximation | p. 116 |
| Applications | p. 120 |
| Recent results on hyperbolic relaxation problems | p. 128 |
| Introduction | p. 128 |
| Motivations | p. 131 |
| The smooth case | p. 141 |
| Discontinuous equilibrium solutions and weak convergence methods | p. 154 |
| The BV framework | p. 168 |
| Lectures on stability of nonlinear waves in viscous media and numerics | p. 199 |
| Introduction | p. 199 |
| Perturbations of constant states | p. 204 |
| Shock waves | p. 216 |
| Rarefaction waves | p. 232 |
| Multigrid methods for flow problems | p. 248 |
| Table of Contents provided by Blackwell. All Rights Reserved. |
ISBN: 9780849306440
ISBN-10: 0849306442
Series: Monographs and Surveys in Pure and Applied Mathematics
Audience:
Professional
Format:
Hardcover
Language:
English
Number Of Pages: 272
Published: 30th December 1998
Dimensions (cm): 25.4 x 17.8
x 2.1
Weight (kg): 0.712
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