Mathematical Biosciences and Engineering, 2009, 6(1): 83-91. doi: 10.3934/mbe.2009.6.83.

Primary: 35K65, 35B25; Secondary: 34C37

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

1. Department of Mathematics, Faculty of Science, South Valley University, Qen


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.
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Keywords reaction-diffusion-advection equations; bacterial growth; traveling wave fronts; numerical approximations

Citation: M. B. A. Mansour. Computation of traveling wave fronts for a nonlinear diffusion-advection model. Mathematical Biosciences and Engineering, 2009, 6(1): 83-91. doi: 10.3934/mbe.2009.6.83


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