Hyperbolic conservation laws on manifolds with limited regularity

Lefloch, Philippe; Okutmustur, BAVER

doi:10.1016/j.crma.2008.03.017

Hyperbolic conservation laws on manifolds with limited regularity

Lefloch P. G., Okutmustur B.

COMPTES RENDUS MATHEMATIQUE, cilt.346, ss.539-543, 2008 (SCI-Expanded, Scopus)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 346
Basım Tarihi: 2008
Doi Numarası: 10.1016/j.crma.2008.03.017
Dergi Adı: COMPTES RENDUS MATHEMATIQUE
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Sayfa Sayıları: ss.539-543
Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
Orta Doğu Teknik Üniversitesi Adresli: Hayır

We introduce a formulation of the initial and boundary value problem for nonlinear hyperbolic conservation laws posed on a differential manifold endowed with a volume form, possibly with a boundary; in particular, this includes the important case of Lorentzian manifolds. Only limited regularity is assumed on the geometry of the manifold. For this problem, we establish the existence and uniqueness of an L-1 semi-group of weak solutions satisfying suitable entropy and boundary conditions.

We introduce a formulation of the initial and boundary value problem for nonlinear hyperbolic conservation laws posed on a differential manifold endowed with a volume form, possibly with a boundary; in particular, this includes the important case of Lorentzian manifolds. Only limited regularity is assumed on the geometry of the manifold. For this problem, we establish the existence and uniqueness of an L1 semi-group of weak solutions satisfying suitable entropy and boundary conditions.