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.
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