Summary and Info
The present Cime volume includes 4 lecture courses by Bressan, Serre, Zumbrun and Williams and a Tutorial by Bressan on the Center Manifold Theorem. Bressan’s notes start with an extensive review 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’ lectures describe the stability of multidimensional viscous shocks. Zumbrun discusses planar stability for viscous shocks with a realistic physical viscosity, and necessary and sufficient conditions for nonlinear stability.
More About the Author
Alberto Bressan (born 15 June 1956) is an Italian mathematician at Penn State University. His primary field of research is mathematical analysis including hyperbolic systems of conservation laws, impulsive control of Lagrangian systems, and non-cooperative differential games.
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Hyperbolic systems of balance laws: lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 14-21, 2003 0 out of 5 stars based on 0 ratings.