Long-time behavior of scalar viscous shock fronts in two dimensions

被引：30

作者：

Goodman J. ^{[1
]}

Miller J.R. ^{[2
]}

机构：

[1] Courant Institute of Mathematical Sciences, New York University, New York

[2] Department of Mathematics, Georgetown University, Washington

来源：

Journal of Dynamics and Differential Equations | 1999年 / 11卷 / 2期

关键词：

Long-time behavior; Shock fronts; Viscous conservation law;

D O I：

10.1023/A:1021977329306

中图分类号：

学科分类号：

摘要：

We prove nonlinear stability in L1 of planar shock front solutions to a viscous conservation law in two spatial dimensions and obtain an expression for the asymptotic form of small perturbations. The leading-order behavior is shown rigorously to be governed by an effective diffusion coefficient depending on forces transverse to the shock front. The proof is based on a spectral analysis of the linearized problem. © 1999 Plenum Publishing Corporation.

引用

页码：255 / 277

页数：22

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