Abstract
A quadratic interaction potential \(t \mapsto \Upsilon (t)\) for hyperbolic systems of conservation laws is constructed, whose value \(\Upsilon (\bar{t})\) at time \(\bar{t}\) depends only on the present and the future profiles of the solution and not on the past ones. Such potential is used to bound the change of the speed of the waves at each interaction.
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This article is part of the topical collection “Hyperbolic PDEs, Fluids, Transport and Applications: Dedicated to Alberto Bressan for his 60th birthday” guest edited by Fabio Ancona, Stefano Bianchini, Pierangelo Marcati, Andrea Marson.
The author would like to thank Prof. Stefano Bianchini for many helpful discussions about the topic of this paper.
The paper was submitted while the author was a Post-Doc at the MPI for Mathematics in the Sciences in Leipzig.
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Modena, S. A “forward-in-time” quadratic potential for systems of conservation laws. Nonlinear Differ. Equ. Appl. 24, 53 (2017). https://doi.org/10.1007/s00030-017-0476-4
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DOI: https://doi.org/10.1007/s00030-017-0476-4