A “forward-in-time” quadratic potential for systems of conservation laws

A “forward-in-time” quadratic potential for systems of conservation laws A quadratic interaction potential $$t \mapsto \Upsilon (t)$$ t ↦ Υ ( t ) for hyperbolic systems of conservation laws is constructed, whose value $$\Upsilon (\bar{t})$$ Υ ( t ¯ ) at time $$\bar{t}$$ 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Differential Equations and Applications NoDEA Springer Journals

A “forward-in-time” quadratic potential for systems of conservation laws

, Volume 24 (5) – Aug 14, 2017
23 pages

Publisher
Springer International Publishing
Subject
Mathematics; Analysis
ISSN
1021-9722
eISSN
1420-9004
D.O.I.
10.1007/s00030-017-0476-4
Publisher site
See Article on Publisher Site

Abstract

A quadratic interaction potential $$t \mapsto \Upsilon (t)$$ t ↦ Υ ( t ) for hyperbolic systems of conservation laws is constructed, whose value $$\Upsilon (\bar{t})$$ Υ ( t ¯ ) at time $$\bar{t}$$ 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.

Journal

Nonlinear Differential Equations and Applications NoDEASpringer Journals

Published: Aug 14, 2017

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