This paper utilizes a nonlinear reaction-diffusion-advection model
for describing the spatiotemporal evolution of bacterial growth. The
traveling wave solutions of the corresponding system of partial
differential equations are analyzed. Using two methods, we then find
such solutions numerically. One of the methods involves the
traveling wave equations and solving an initial-value problem, which
leads to accurate computations of the wave profiles and speeds. The
second method is to construct time-dependent solutions by
solving an initial-moving boundary-value problem for the PDE system,
showing another approximation for such wave solutions.
Citation: M. B. A. Mansour. Computation of traveling wave fronts for a nonlinear diffusion-advection model[J]. Mathematical Biosciences and Engineering, 2009, 6(1): 83-91. doi: 10.3934/mbe.2009.6.83
Abstract
This paper utilizes a nonlinear reaction-diffusion-advection model
for describing the spatiotemporal evolution of bacterial growth. The
traveling wave solutions of the corresponding system of partial
differential equations are analyzed. Using two methods, we then find
such solutions numerically. One of the methods involves the
traveling wave equations and solving an initial-value problem, which
leads to accurate computations of the wave profiles and speeds. The
second method is to construct time-dependent solutions by
solving an initial-moving boundary-value problem for the PDE system,
showing another approximation for such wave solutions.