Hyperbolic Systems of Balance Laws : Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 14–21, 2003 / by Alberto Bressan, Denis Serre, Mark Williams, Kevin Zumbrun ; edited by Pierangelo Marcati
(Lecture Notes in Mathematics ; 1911)
| データ種別 | 電子ブック |
|---|---|
| 出版情報 | Berlin, Heidelberg : Springer Berlin Heidelberg , 2007 |
| 本文言語 | 英語 |
| 大きさ | XII, 356 p : online resource |
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| 内容注記 | BV Solutions to Hyperbolic Systems by Vanishing Viscosity Discrete Shock Profiles: Existence and Stability Stability of Multidimensional Viscous Shocks Planar Stability Criteria for Viscous Shock Waves of Systems with Real Viscosity |
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| 一般注記 | The present Cime volume includes four lectures by Bressan, Serre, Zumbrun and Williams and an appendix with a Tutorial on Center Manifold Theorem by Bressan. Bressan’s notes start with an extensive review of the theory of hyperbolic conservation laws. Then he introduces the vanishing viscosity approach and explains clearly the building blocks of the theory in particular the crucial role of the decomposition by travelling waves. Serre focuses on existence and stability for discrete shock profiles, he reviews the existence both in the rational and in the irrational cases and gives a concise introduction to the use of spectral methods for stability analysis. Finally the lectures by Williams and Zumbrun deal with the stability of multidimensional fronts. Williams’ lecture describes the stability of multidimensional viscous shocks: the small viscosity limit, linearization and conjugation, Evans functions, Lopatinski determinants etc. Zumbrun discusses planar stability for viscous shocks with a realistic physical viscosity, necessary and sufficient conditions for nonlinear stability, in analogy to the Lopatinski condition obtained by Majda for the inviscid case |
| 著者標目 | *Bressan, Alberto author Serre, Denis author Williams, Mark author Zumbrun, Kevin author Marcati, Pierangelo editor SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Partial differential equations LCSH:Numerical analysis LCSH:Continuum physics FREE:Mathematics FREE:Partial Differential Equations FREE:Classical Continuum Physics FREE:Numerical Analysis |
| 分 類 | DC23:515.353 |
| 巻冊次 | ISBN:9783540721871 
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| ISBN | 9783540721871 |
| URL | http://dx.doi.org/10.1007/978-3-540-72187-1 |
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