Rate of convergence of solutions to traveling fronts for some quasi-linear relaxation systems with viscous

Abstract

This paper is concerned with the exponential convergence rates of solutions to non-degenerate traveling fronts in some exponentially weighted spaces and the algebraic convergence rates of solutions to non-degenerate and degenerate traveling fronts in some algebraically weighted spaces for quasi-linear relaxation systems with small viscous using weighted energy method, where the small initial perturbations of the traveling fronts are in some appropriate weighted spaces and the wave strengths are small.

Keywords:

• Traveling fronts
• exponential decay
• algebraic decay
• weighted spaces

AMS Subject Classifications:

• 35B30
• 35B40
• 35L65
• 76L05
• 90B20

Acknowledgements

The author is very grateful to Prof. Yaping Wu for her guidance, useful advice and constant encouragement. The author is also grateful to Jingyu Li for valuable discussion.

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was partially supported by the National Nature Science Foundation of China [grant number 11471221], [grant number 11501016]; BTBU Foundation [grant number QNJJ2015-16]; Beijing Municipal Education Commission [KZ201310028030].