Archive for Rational Mechanics and Analysis

, Volume 175, Issue 2, pp 245–267

Divergence-Measure Fields, Sets of Finite Perimeter, and Conservation Laws

Article

DOI: 10.1007/s00205-004-0346-1

Cite this article as:
Chen, GQ. & Torres, M. Arch. Rational Mech. Anal. (2005) 175: 245. doi:10.1007/s00205-004-0346-1

Abstract.

Divergence-measure fields in L over sets of finite perimeter are analyzed. A notion of normal traces over boundaries of sets of finite perimeter is introduced, and the Gauss-Green formula over sets of finite perimeter is established for divergence-measure fields in L. The normal trace introduced here over a class of surfaces of finite perimeter is shown to be the weak-star limit of the normal traces introduced in Chen & Frid [6] over the Lipschitz deformation surfaces, which implies their consistency. As a corollary, an extension theorem of divergence-measure fields in L over sets of finite perimeter is also established. Then we apply the theory to the initial-boundary value problem of nonlinear hyperbolic conservation laws over sets of finite perimeter.

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Department of MathematicsNorthwestern UniversityEvanstonUSA