| Titre de série : |
Systems of conservation laws, 1 |
| Titre : |
Hyperbolicity, entropies, shock waves |
| Type de document : |
texte imprimé |
| Auteurs : |
Denis Serre (1954-...), Auteur ; Ian Naismith Sneddon (1919-2000), Traducteur |
| Editeur : |
Cambridge ; New York ; Melbourne [UK ; USA] : Cambridge University Press (CUP) |
| Année de publication : |
1999, cop. 1999 |
| Importance : |
1 vol. (xxii-263 p.) |
| Présentation : |
fig. |
| Format : |
25 cm |
| ISBN/ISSN/EAN : |
978-0-521-58233-9 |
| Note générale : |
Titre original : Systèmes de lois de conservation. I, hyperbolicité, entropies, ondes de choc -- PPN 070830681 -- ISBN : 0-521-58233-4 (rel.) . |
| Langues : |
Anglais (eng) |
| Tags : |
Lois de conservation (physique) -- Mathématiques Entropie Ondes de choc Physique mathématique Conservation laws (Physics) -- Mathematics Entropy Shock waves Mathematical physics Real and Complex Analysis |
| Index. décimale : |
515.35 Équations différentielles. Problème de Cauchy. Ordres et degrés. Problèmes aux limites (généralités). Théories de la bifurcation, de la perturbation, de la stabilité |
| Résumé : |
Systems of conservation laws arise naturally in physics and chemistry. To understand them and their consequences (shock waves, finite velocity wave propagation) properly in mathematical terms requires, however, knowledge of a broad range of topics. This book sets up the foundations of the modern theory of conservation laws, describing the physical models and mathematical methods, leading to the Glimm scheme. Building on this the author then takes the reader to the current state of knowledge in the subject. The maximum principle is considered from the viewpoint of numerical schemes and also in terms of viscous approximation. Small waves are studied using geometrical optics methods. Finally, the initial-boundary problem is considered in depth. Throughout, the presentation is reasonably self-contained, with large numbers of exercises and full discussion of all the ideas. This will make it ideal as a text for graduate courses in the area of partial differential equations. [source : 4ème de couv.] |
| Note de contenu : |
1 - Some models (pp 1-24) -- 2 - Scalar equations in dimension d = 1 (pp 25-67) - 3 - Linear and quasi-linear systems (pp 68-105) - 4 - Dimension d = 1, the Riemann problem (pp 106-145) - 5 - The Glimm scheme (pp 146-185) - 6 - Second order perturbations (pp 186-219) - 7 - Viscosity profiles for shock waves (pp 220-254) - Bibliogr. p. 255-260. Index p.261-263 |
Systems of conservation laws, 1. Hyperbolicity, entropies, shock waves [texte imprimé] / Denis Serre (1954-...), Auteur ; Ian Naismith Sneddon (1919-2000), Traducteur . - Cambridge ; New York ; Melbourne (UK ; USA) : Cambridge University Press (CUP), 1999, cop. 1999 . - 1 vol. (xxii-263 p.) : fig. ; 25 cm. ISBN : 978-0-521-58233-9 Titre original : Systèmes de lois de conservation. I, hyperbolicité, entropies, ondes de choc -- PPN 070830681 -- ISBN : 0-521-58233-4 (rel.) . Langues : Anglais ( eng)
| Tags : |
Lois de conservation (physique) -- Mathématiques Entropie Ondes de choc Physique mathématique Conservation laws (Physics) -- Mathematics Entropy Shock waves Mathematical physics Real and Complex Analysis |
| Index. décimale : |
515.35 Équations différentielles. Problème de Cauchy. Ordres et degrés. Problèmes aux limites (généralités). Théories de la bifurcation, de la perturbation, de la stabilité |
| Résumé : |
Systems of conservation laws arise naturally in physics and chemistry. To understand them and their consequences (shock waves, finite velocity wave propagation) properly in mathematical terms requires, however, knowledge of a broad range of topics. This book sets up the foundations of the modern theory of conservation laws, describing the physical models and mathematical methods, leading to the Glimm scheme. Building on this the author then takes the reader to the current state of knowledge in the subject. The maximum principle is considered from the viewpoint of numerical schemes and also in terms of viscous approximation. Small waves are studied using geometrical optics methods. Finally, the initial-boundary problem is considered in depth. Throughout, the presentation is reasonably self-contained, with large numbers of exercises and full discussion of all the ideas. This will make it ideal as a text for graduate courses in the area of partial differential equations. [source : 4ème de couv.] |
| Note de contenu : |
1 - Some models (pp 1-24) -- 2 - Scalar equations in dimension d = 1 (pp 25-67) - 3 - Linear and quasi-linear systems (pp 68-105) - 4 - Dimension d = 1, the Riemann problem (pp 106-145) - 5 - The Glimm scheme (pp 146-185) - 6 - Second order perturbations (pp 186-219) - 7 - Viscosity profiles for shock waves (pp 220-254) - Bibliogr. p. 255-260. Index p.261-263 |
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Systems of conservation laws, 1. Hyperbolicity, entropies, shock waves (1999, cop. 1999)