Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

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

Pages: 4735 - 4749, Volume 34, Issue 11, November 2014      doi:10.3934/dcds.2014.34.4735

       Abstract        References        Full Text (429.1K)       Related Articles       

Cunming Liu - School of Mathematics, Taiyuan University of Technology, Shanxi, 030024, China (email)
Jianli Liu - Department of Mathematics, Shanghai University, Shanghai 200444, China (email)

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.

Received: July 2013;      Revised: March 2014;      Available Online: May 2014.