Divergence-measure fields, sets of finite perimeter, and conservation laws

Journal article

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 and 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.

Authors: Chen, G; Torres, M

• Journal: Archive for Rational Mechanics and Analysis
• Volume: 175
• Issue: 2
• Pages: 245-267
• Publication date: 2005-02-01
• DOI: 10.1007/s00205-004-0346-1
• EISSN: 1432-0673
• ISSN: 0003-9527