On the existence and compactness of a twodimensional resonant system of conservation laws
| Venue: | Commun. Math. Sci |
| Citations: | 9 - 3 self |
BibTeX
@ARTICLE{Karlsen_onthe,
author = {Kenneth H. Karlsen and Michel Rascle and Eitan Tadmor},
title = {On the existence and compactness of a twodimensional resonant system of conservation laws},
journal = {Commun. Math. Sci},
year = {},
pages = {253--265}
}
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Abstract
Abstract. We prove the existence of a weak solution to a two-dimensional resonant 3×3 system of conservation laws with BV initial data. Due to possible resonance (coinciding eigenvalues), spatial BV estimates are in general not available. Instead, we use an entropy dissipation bound combined with the time translation invariance property of the system to prove existence based on a two-dimensional compensated compactness argument adapted from [E. Tadmor, M. Rascle, and P. Bagnerini, Compensated compactness for 2D conservation laws, J. Hyperbolic Differ. Equ., 2(3), 697-712, 2005]. Existence is proved under the assumption that the flux functions in the two directions are linearly independent. Key words. Nonlinear conservation laws, multi-dimensional, discontinuous fluxes, entropy bounds, weak solutions, existence, compensated compactness AMS subject classifications. 35L65, 35L80 1.
