[ 1996 | 1997 | 1998 | 1999 | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | All | Home ]

Preprint 2015-012

High frequency waves and the maximal smoothing effect for nonlinear scalar conservation laws

Stephane Junca

Abstract: The article first studies the propagation of well prepared high frequency waves with small amplitude ε near constant solutions for entropy solutions of multidimensional nonlinear scalar conservation laws. Second, such oscillating solutions are used to highlight a conjecture of Lions, Perthame, Tadmor, ([23]), about the maximal regularizing effect for nonlinear conservation laws. For this purpose, a definition of smooth nonlinear flux is stated and compared to classical definitions. Then it is proved that the uniform smoothness expected by [23] in Sobolev spaces cannot be exceeded for all smooth nonlinear fluxes.

Reference
[23] P.-L. Lions, B. Perthame, E. Tadmor, A kinetic formulation of multidimensional scalar conservation laws and related equations, J. Amer. Math. Soc. 7, (1994), 169–192 [MR1201239].
Paper:
Available as PDF (533 Kbytes).
Author(s):
Stephane Junca ,
Publishing information:
Published in SIAM J. Math. Anal. 46 no. 3, 2160-2184, (2014) [MR224578].
Submitted by:
; 2015-04-16.