A kinetic approach to scalar multidimensional conservation laws. (English) Zbl 0880.35069
Summary: This paper gives the kinetic formulation of multidimensional conservation laws and proves the compactness of velocity averages by employing the compactness theorem in \(L^1_{\text{loc}}(\mathbb{R}^n\times \mathbb{R}_t)\). As a byproduct, the existence and uniqueness of the generalized solution is obtained.
MSC:
35L65 | Hyperbolic conservation laws |
35L45 | Initial value problems for first-order hyperbolic systems |