Stability of traveling wave solutions to Cauchy problem of diagnolizable quasilinear hyperbolic systems

Cunming Liu; Jianli Liu

doi:10.3934/dcds.2014.34.4735

Article Contents

2014, Volume 34, Issue 11: 4735-4749. Doi: 10.3934/dcds.2014.34.4735

This issue Previous Article On some Liouville type theorems for the compressible Navier-Stokes equations Next Article Non-normal numbers in dynamical systems fulfilling the specification property

Stability of traveling wave solutions to Cauchy problem of diagnolizable quasilinear hyperbolic systems

Cunming Liu^1, and
Jianli Liu^2,

1.
School of Mathematics, Taiyuan University of Technology, Shanxi, 030024
2.
Department of Mathematics, Shanghai University, Shanghai 200444

Received: June 30, 2013

Revised: February 28, 2014

Published: October 2014

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Abstract

In this paper we consider the existence and stability of traveling wave solutions to Cauchy problem of diagonalizable quasilinear hyperbolic systems. Under the appropriate small oscillation assumptions on the initial traveling waves, we derive the stability result of the traveling wave solutions, especially for intermediate traveling waves. As the important examples, we will apply the results to some systems arising in fluid dynamics and elementary particle physics.

Keywords:

Diagonalizable quasilinear hyperbolic system,
traveling wave solution,
linearly degenerate,
classical solution,
stability.

Mathematics Subject Classification: Primary: 35C07, 37C75; Secondary: 35L45.

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