In this chapter we introduce the definitions of hyperbolicity and strict hyperbolicity and generalize the definitions given in the previous chapters to the case of general systems of conservation laws in one space dimension. In the last two sections we also show how to construct a weak solution to the Cauchy problem for a strictly hyperbolic system of conservation laws with constant coefficient and to the Riemann problem for a strictly hyperbolic system of conservation laws with genuinely nonlinear or linearly degenerate characteristic fields. We prove also the local existence of a weak solution to the Riemann problem for a general system, when the initial states are sufficiently close.
One-Dimensional Systems of Conservation Laws
Understanding Complex Systems
Macroscopic Models for Vehicular Flows and Crowd Dynamics: Theory and Applications ; Chapter : 7 ; 93-110
2013-01-01
18 pages
Article/Chapter (Book)
Electronic Resource
English
One-Dimensional Scalar Conservation Laws
Springer Verlag | 2013
|Conservation laws of linear, homogeneous systems
TIBKAT | 1970
|Spacedrives and Conservation Laws
AIAA | 2018
|