Dafermos C.M. Hyperbolic Conservation Laws in Continuum Physics

Grundlehren der Mathematischen Wissenschaften, Springer-Verlag, Berlin, 1999, 443 p.This masterly exposition of the mathematical theory of hyperbolic system laws brings out the intimate connection with continuum thermodynamics, emphasizing issues in which the analysis may reveal something about the physics and, in return, the underlying physical structure may direct and drive the analysis. The reader should have a certain mathematical sophistication and be familiar with the rudiments of the qualitative theory of partial differential equations, whereas the required notions from continuum physics are introduced from scratch.