$L^p$ asymptotic behavior of perturbed viscous shock profiles
| dc.creator | Raoofi, Mohammadreza | |
| dc.date | 2004-08-17 | |
| dc.date.accessioned | 2026-07-07T05:11:19Z | |
| dc.date.available | 2026-07-07T05:11:19Z | |
| dc.description | We investigate the $L^p $ asymptotic behavior $(1\le p \le \infty)$ of a perturbation of a Lax or overcompressive type shock wave solution to a system of conservation law in one dimension. The system of the equations can be strictly parabolic, or have real viscosity matrix (partially parabolic, e.g., compressible Navier--Stokes equations or equations of Magnetohydrodynamics). We use known pointwise Green function bounds for the linearized equation around the shock to show that the perturbation of such a solution can be decomposed into a part corresponding to shift in shock position or shape, a part which is the sum of diffusion waves, i.e., the solutions to a viscous Burger's equation, conserving the initial mass and convecting away from the shock profile in outgoing modes, and another part which is more rapidly decaying in $L^p$. | |
| dc.description | 59 pp | |
| dc.identifier | https://arxiv.org/abs/math/0408227 | |
| dc.identifier | http://arxiv.org/abs/math/0408227 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72204 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35L65 (35B25 35B30 35K65) | |
| dc.title | $L^p$ asymptotic behavior of perturbed viscous shock profiles | |
| dc.type | text |