Stability of traveling wavefronts for time-delayed reaction-diffusion equations

Ming Mei

doi:10.3934/proc.2009.2009.526

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2009, Volume 2009: 526-535. Doi: 10.3934/proc.2009.2009.526 open access

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Stability of traveling wavefronts for time-delayed reaction-diffusion equations

Ming Mei^1,

1.
Department of Mathematics, Champlain College Saint-Lambert, Saint-Lambert, Quebec, J4P 3P2

Received: May 31, 2008

Revised: March 31, 2009

Published: August 2009

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Abstract

This paper is concerned with time-delayed reaction-diffusion equations. For all traveling wavefronts, they are proved to be stable time-asymptotically by the technical weighted energy method with the comparison principle together, which extends the wave stability results obtained in [7,8]. Some numerical simulations are also carried out, which confirm our theoretical results.

Keywords:

traveling wavefronts,
stability,
time-delayed reaction diffusion equations,
Nicolson's blowflies equation.

Mathematics Subject Classification: Primary: 35K57; Secondary: 34K20, 92D25.

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