American Institute of Mathematical Sciences

Advanced
2009, 6(1): 83-91. doi: 10.3934/mbe.2009.6.83

Computation of traveling wave fronts for a nonlinear diffusion-advection model

M. B. A. Mansour 1,

1. 

Department of Mathematics, Faculty of Science, South Valley University, Qen, Egypt

Received  November 2007 Revised  August 2008 Published  December 2008

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.
Keywords: reaction-diffusion-advection equations; bacterial growth; traveling wave fronts; numerical approximations.
Mathematics Subject Classification: Primary: 35K65, 35B25; Secondary: 34C37.
Citation: M. B. A. Mansour. Computation of traveling wave fronts for a nonlinear diffusion-advection model. Mathematical Biosciences & Engineering, 2009, 6 (1) : 83-91. doi: 10.3934/mbe.2009.6.83
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