Formation of compression waves with multiscale asymptotics in the Burgers and KdV models
Mathematical Physics
2015-05-06 v1 math.MP
Abstract
The Cauchy problem for the Burgers equation with a small dissipation and an initial weak discontinuity and the Cauchy problem with a large initial gradient for a quasilinear parabolic equation and for the Korteweg-de Vries (KdV) equation are considered. Multiscale asymptotics of solutions corresponding to shock waves are constructed. Some results can also be applied to rarefaction waves.
Keywords
Cite
@article{arxiv.1505.00868,
title = {Formation of compression waves with multiscale asymptotics in the Burgers and KdV models},
author = {Sergei V. Zakharov},
journal= {arXiv preprint arXiv:1505.00868},
year = {2015}
}
Comments
Keywords: Burgers equation, KdV equation, Cauchy problem, multiscale asymptotics, weak discontinuity, shock waves, renormalization. 12 pages