Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Some paradoxical effects of the advection on a class of diffusive equations in Ecology

Pages: 3031 - 3056, Volume 19, Issue 10, December 2014      doi:10.3934/dcdsb.2014.19.3031

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David Aleja - Department of Mathematics, University Carlos III of Madrid, Leganés (Madrid), 28911, Spain (email)
Julián López-Gómez - Department of Applied Mathematics, Complutense University of Madrid, Madrid, 28040, Spain (email)

Abstract: In this paper we refine in a substantial way part of the materials of the celebrated paper of Belgacem and Cosner [3] by considering a rather general class of degenerate diffusive logistic equations in the presence of advection. Rather paradoxically, a large advection can provoke the stabilization to an steady state of a former explosive solution. Similarly, even with a severe taxis down the environmental gradient the species can be permanent.

Keywords:  Advection, diffusive logistic equations, dynamics.
Mathematics Subject Classification:  Primary: 35K20, 35K58; Secondary: 35P15.

Received: July 2013;      Revised: September 2013;      Available Online: October 2014.