Lengeler, Daniel and Mueller, Thomas (2013) Scalar conservation laws on constant and time-dependent Riemannian manifolds. JOURNAL OF DIFFERENTIAL EQUATIONS, 254 (4). pp. 1705-1727. ISSN 0022-0396, 1090-2732
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In this paper we establish well-posedness for scalar conservation laws on closed manifolds M endowed with a constant or a time-dependent Riemannian metric for initial values in L-infinity(M). In particular we show the existence and uniqueness of entropy solutions as well as the L-1 contraction property and a comparison principle for these solutions. Throughout the paper the flux function is allowed to depend on time and to have non-vanishing divergence. Furthermore, we derive estimates of the total variation of the solution for initial values in BV(M), and we give, in the case of a time-independent metric, a simple geometric characterisation of flux functions that give rise to total variation diminishing estimates. (C) 2012 Elsevier Inc. All rights reserved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | SHALLOW-WATER EQUATIONS; WELL-POSEDNESS; EXISTENCE; WAVES; Hyperbolic; Conservation laws; Riemannian manifolds; Measure-valued solutions; Shock waves |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 28 Apr 2020 09:00 |
| Last Modified: | 28 Apr 2020 09:00 |
| URI: | https://pred.uni-regensburg.de/id/eprint/17146 |
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