Novel stability results for traveling wavefronts in an age-structured reaction-diffusion equation

Abstract

For a time-delayed reaction-diffusion equation of age-structuredsingle species population, the linear and nonlinear stability ofthe traveling wavefronts were proved by Gourley [4] andLi-Mei-Wong [8] respectively. The stability results,however, assume the delay-time is sufficiently small. We now provethat the wavefronts remain stable even when the delay-time isarbitrarily large. This essentially improves the previousstability results obtained in [4, 8]. Finally, we point outthat this novel stability can be applied to the age-structuredreaction-diffusion equation with a more general maturation rate.

Keywords

• travelingwavefronts
• time-delayed reaction-diffusion equation
• exponential decay rate.
• nonlinear stability