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

  • Received: 01 November 2007 Accepted: 29 June 2018 Published: 01 December 2008
  • MSC : Primary: 35K65, 35B25; Secondary: 34C37

  • 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

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  • 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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    © 2009 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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