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    • On the sharp front-type solution of the Nagumo equation with nonlinear diffusion and convection

      M B A Mansour

      Research Articles Volume 80 Issue 3 March 2013 pp 533-538

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pram/080/03/0533-0538

    • Keywords

       

      Nagumo equation; nonlinear degenerate diffusion; nonlinear convection; sharp wavefront solution; minimum wave speed.

    • Abstract

       

      This paper is concerned with the Nagumo equation with nonlinear degenerate diffusion and convection which arises in several problems of population dynamics, chemical reactions and others. A sharp front-type solution with a minimum speed to this model equation is analysed using different methods. One of the methods is to solve the travelling wave equations and compute an exact solution which describes the sharp travelling wavefront. The second method is to solve numerically an initial-moving boundary-value problem for the partial differential equation and obtain an approximation for this sharp front-type solution.

    • Author Affiliations

       

      M B A Mansour1 2

      1. Department of Mathematics, Faculty of Science at Qena, South Valley University, Qena, Egypt
      2. Department of Mathematics, University College at Al-Qunfudah, Umm Al-Qura University, Mecca, Saudi Arabia

    • Dates

       
      Published
      March 2013
      Manuscript received
      1 November 2011
      Manuscript revised
      30 July 2012
      Accepted
      22 August 2012

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