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A counter‐example concerning regularity properties for systems of conservation laws
Author(s) -
Caravenna Laura,
Spinolo Laura V.
Publication year - 2015
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201510302
Subject(s) - conservation law , geodetic datum , classification of discontinuities , scalar (mathematics) , mathematics , property (philosophy) , pure mathematics , mathematical economics , mathematical analysis , geography , philosophy , geometry , epistemology , cartography
We exhibit an explicit counter‐example which rules the possibility of extending to systems of conservation laws a regularity property of scalar conservation laws known as Schaeffer's Theorem. Loosely speaking, Schaeffer's Regularity Theorem asserts that, for a generic smooth initial datum, the solution of the Cauchy problem can develop at most finitely many discontinuities on compact sets. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)