TY  - BOOK
AU  - Bressan,Alberto
AU  - Serre,Denis
AU  - Williams,Mark
AU  - Zumbrun,Kevin
AU  - Marcati,Pierangelo
ED  - SpringerLink (Online service)
TI  - Hyperbolic Systems of Balance Laws: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 14–21, 2003 
T2  - C.I.M.E. Foundation Subseries
SN  - 9783540721871
AV  - QA370-380 
U1  - 515.353 23
PY  - 2007///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Differential equations, partial
KW  - Numerical analysis
KW  - Partial Differential Equations
KW  - Classical and Continuum Physics
KW  - Numerical Analysis
N1  - 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
N2  - 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
UR  - https://doi.org/10.1007/978-3-540-72187-1
ER  -