High frequency waves and the maximal smoothing effect for nonlinear scalar conservation laws
Analysis of PDEs
2013-02-12 v1
Abstract
The article first studies the propagation of well prepared high frequency waves with small amplitude 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, (1994), about the maximal regularizing effect for nonlinear conservation laws. For this purpose, a new definition of nonlinear flux is stated and compared to classical definitions. Then it is proved that the smoothness expected in Sobolev spaces cannot be exceeded.
Cite
@article{arxiv.1302.2590,
title = {High frequency waves and the maximal smoothing effect for nonlinear scalar conservation laws},
author = {Stéphane Junca},
journal= {arXiv preprint arXiv:1302.2590},
year = {2013}
}
Comments
28 pp