Hyperbolic Systems of Balance Laws
This volume includes the lecture notes delivered at the CIME Course “Hyp- bolic Systems of Balance Laws” held July 14-21, 2003 in Cetraro (Cosenza, Italy). The present volume includes lectures notes by A. Bressan, D. Serre, K. Zumbrun and M. Williams and an appendix by A. Bressan on the center manifoldtheorem.Theseareamongthe“hottopics”inthis?eldandcanbeof great interest, not only to professional mathematicians, but also for physicists and engineers. The concept of hyperbolic systems of balance laws was introduced by the works of natural philosophers of the eighteenth century, predominantly L. Euler (1755), and has over the past one hundred and ?fty years become the naturalframeworkforthestudyofgasdynamicsand,morebroadly,ofcont- uumphysics.DuringthisperiodoftimegreatpersonalitieslikeStokes,Challis, Riemann, Rankine, Hugoniot, Lord Rayleigh and later Prandtl, Hadamard, H. Lewy, G.I. Taylor and many others wrote several fundamental papers, thus laying the groundwork for the further development of the mathematical theory. However the ?rst part of the past century did not see much activity on the part of mathematicians in this ?eld and it was only during the S- ond World War, in connection with the Manhattan Project, that associated research received a great impetus. Many important scientists like J. Von Neumann, R. Courant, K.O. Friedrichs, H. Bethe and Ya. Zeldowich became interested in this ?eld and proposed many new key concepts, the in?uence of which remains very great to the present day.