## Majid Bani-Yaghoub, Ph.D.Associate Professor &
Associate Director
Office: Manheim 205 A |
## Numerical Simulations of a Nonlocal Delayed Reaction-Diffusion Model##
3. Impacts of the diffusion rates on wave solutions |

To illustrate the formation and stability of wave solutions we turn our attention to a
class of nonlocal delayed RD equation proposed by So et al (2001, Proc. R. Soc.
Lond. A, 457, 1841–1853). In particular, the
authors adopted Smith-Thieme’s approach to obtain the following model of single
species population.

where x ∈ R, 0 < ε≤ 1, w(x, t) represents the total mature population u(x, a, t) at age a, time t and position x that is given by

The kernel function is given by

As the immature population becomes immobile (i.e. when α → 0), the kernel function f(x) is changed to Dirac delta function and therefore the model reduces to

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**

Convergence to Stationary Wavefront

It is numerically shown that the solution of the
initial value problem corresponding to the model may
converge to the stationary wave front of the model.
** **

blue= PDE Solution

red = Stationary Wavefront

Formation and disappearance of a wave pulse in the 2-dimensional domain for the reduced model

where x ∈ R, 0 < ε≤ 1, w(x, t) represents the total mature population u(x, a, t) at age a, time t and position x that is given by

The kernel function is given by

As the immature population becomes immobile (i.e. when α → 0), the kernel function f(x) is changed to Dirac delta function and therefore the model reduces to

Convergence to Stationary Wavefront

blue= PDE Solution

red = Stationary Wavefront

Formation and disappearance of a wave pulse in the 2-dimensional domain for the reduced model