Equations of hyperbolic type

Abstract

In this chapter we deal with a typical class of problems arising from conservation laws, that is evolution problems of hyperbolic type involving either pure-advection phenomena or advection-reaction ones. We will focus mainly on linear problems in one spatial dimension. The non-linear counterparts of these problems have a great interest in several contexts, but are characterized by specific aspects that go beyond the scope of this text. An excellent introduction to this subject is the book of LeVeque [ LeV90 ], with the accompanying software library ClawPack (see also [ LeV02 ]).