Formation of compression waves with multiscale asymptotics in the Burgers and KdV models

2015/05/05 by Zakharov, Sergei V.
#35K15 #35K59 #35Q53 #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1505.00868

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.

Related

• On nonlinear superposition of shock waves for the KdV-Burgers equation
• Generation of shock waves from localized sources: The case of the Burgers equation
• Estimates for solutions of Burgers type equations and some applications
• On periodic boundary solutions for cylindrical and spherical KdV-Burgers equations
• The L² contraction of solutions with large perturbation in multiple space dimensions from the oscillatory dispersive planar shock