Entropy Principle, Symmetric Hyperbolic Systems and Shock Waves

Abstract

Publisher Summary This chapter discusses entropy principle, symmetric hyperbolic systems and shock waves. The chapter gives relations between two arguments with different conclusions. The former argument is related to a general question of systems of partial differential equations of hyperbolic type; the latter concerns the role of the “entropy principle” in continuum theories. A generic quasi-linear first order system of the type is considered in the chapter. The system is said to be “conservative,” if there exist four vectors F α of R N , such that the matrices A α are gradients of F α with respect to a suitable field. The symmetric system plays an important role concerning the well-posing of the Cauchy problem; in fact there exist some theorems ensuring existence, uniqueness, and continuous dependence for the local Cauchy problem.