Co-existence of traveling waves for a model of microbial growth and competition in a flow reactor

Pages: 883 - 896, Volume 24, Issue 3, July 2009

doi:10.3934/dcds.2009.24.883       Abstract        Full Text (163.6K)       Related Articles

Wenzhang Huang - Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899, United States (email)

Abstract: Consider a reaction-diffusion model for a microbial flow reactor with two competing species. Suppose that the amount of nutrient is input in a constant velocity at one end of the flow reactor and is washed out at the other end of the reactor. We study the dynamical behavior of population growth of these two species. In particular we are interested in the problem on the coexistence of traveling waves that best describes the long time dynamical behavior. By developing shooting method and continuation argument with the aid of an appropriately Liapunov function, we obtain the sufficient conditions for the coexistence of traveling waves as well as the minimum wave speed.

Keywords:  Microbial flow reactor, reaction-diffusion equations, traveling waves, shooting method, continuation argument.
Mathematics Subject Classification:  Primary: 35K55, 35K57; Secondary: 34C37.

Received: January 2008;      Revised: July 2008;      Published: April 2009.