In this chapter we study the Cauchy problems for one-dimensional scalar conservation laws. In particular, we prove that the Cauchy problem is well posed in the class of entropy weak solutions, in the sense that it admits a unique entropy weak solution. The existence of the solutions is proved by the method of wave front tracking. The uniqueness is proved by showing the Kružkov result of the L1 contractiveness of the flow generated by a scalar conservation law.
The Cauchy Problem
Understanding Complex Systems
Macroscopic Models for Vehicular Flows and Crowd Dynamics: Theory and Applications ; Kapitel : 5 ; 51-62
2013-01-01
12 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch
DOAJ | 2018
|DOAJ | 2011
|A generalized quadrature formula for Cauchy integrals
AIAA | 1971
|Improvements on Cauchy Estimation for Linear Scalar Systems
British Library Conference Proceedings | 2010
|