Novel stability results for traveling wavefronts in an age-structured reaction-diffusion equation.
2009
For a time-delayed reaction-diffusion equation of age-structured
single species population, the linear and nonlinear stability of
the traveling wavefronts were proved by Gourley [4] and
Li-Mei-Wong [8] respectively. The stability results,
however, assume the delay-time is sufficiently small. We now prove
that the wavefronts remain stable even when the delay-time is
arbitrarily large. This essentially improves the previous
stability results obtained in [4, 8]. Finally, we point out
that this novel stability can be applied to the age-structured
reaction-diffusion equation with a more general maturation rate.
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