Hyperbolic conservation laws on manifolds with limited regularity

Download

index.pdf

Date

2008-05-01

Author

Lefloch, Philippe G.
Okutmuştur, Baver

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

186
views

62
downloads

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.

Subject Keywords

General Mathematics

URI

https://hdl.handle.net/11511/41652

Journal

COMPTES RENDUS MATHEMATIQUE

DOI

https://doi.org/10.1016/j.crma.2008.03.017

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Hyperbolic conservation laws on manifolds. An error estimate for finite volume schemes Lefloch, Philippe G.; Okutmuştur, Baver; Neves, Wladimir (Springer Science and Business Media LLC, 2009-07-01) Following Ben-Artzi and LeFloch, we consider nonlinear hyperbolic conservation laws posed on a Riemannian manifold, and we establish an L (1)-error estimate for a class of finite volume schemes allowing for the approximation of entropy solutions to the initial value problem. The error in the L (1) norm is of order h (1/4) at most, where h represents the maximal diameter of elements in the family of geodesic triangulations. The proof relies on a suitable generalization of Cockburn, Coquel, and LeFloch's theo...
REGULARITY OF QUOTIENTS OF DRINFELD MODULAR SCHEMES Kondo, Satoshi; Yasuda, Seidai (Mathematical Sciences Publishers, 2020-02-01) Let A be the coordinate ring of a projective smooth curve over a finite field minus a closed point. For a nontrivial ideal I subset of A, Drinfeld defined the notion of structure of level I on a Drinfeld module.
Chirality of real non-singular cubic fourfolds and their pure deformation classification Finashin, Sergey (Springer Science and Business Media LLC, 2020-02-22) In our previous works we have classified real non-singular cubic hypersurfaces in the 5-dimensional projective space up to equivalence that includes both real projective transformations and continuous variations of coefficients preserving the hypersurface non-singular. Here, we perform a finer classification giving a full answer to the chirality problem: which of real non-singular cubic hypersurfaces can not be continuously deformed to their mirror reflection.
On entire rational maps of real surfaces Ozan, Yıldıray (The Korean Mathematical Society, 2002-01-01) In this paper, we define for a component X-0 of a nonsingular compact real algebraic surface X the complex genus of X-0, denoted by g(C)(X-0), and use this to prove the nonexistence of nonzero degree entire rational maps f : X-0 --> Y provided that g(C)(Y) > g(C)(X-0), analogously to the topological category. We construct connected real surfaces of arbitrary topological genus with zero complex genus.
Relative topology of real algebraic varieties in their complexifications Ozan, Yıldıray (Mathematical Sciences Publishers, 2004-12-01) We investigate, for a given smooth closed manifold M, the existence of an algebraic model X for M (i.e., a nonsingular real algebraic variety diffeomorphic to M) such that some nonsingular projective complexification i:X-->X-C of X admits a retraction r:X-C-->X. If such an X exists, we show that M must be formal in the sense of Sullivan's minimal models, and that all rational Massey products on M are trivial.

Citation Formats

P. G. Lefloch and B. Okutmuştur, “Hyperbolic conservation laws on manifolds with limited regularity,” COMPTES RENDUS MATHEMATIQUE, pp. 539–543, 2008, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/41652.