The non-monotonicity of the KPP speed with respect to diffusion in the presence of a shear flow
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Abstract:
In this paper, we prove via counterexamples that adding an advection term of the form Shear flow (whose streamlines are parallel to the direction of propagation) to a reaction-diffusion equation will be enough heterogeneity to spoil the increasing behavior of the KPP speed of propagation with respect to diffusion. The non-monotonicity of the speed with respect to diffusion will occur even when the reaction term and the diffusion matrices are considered homogeneous (do not depend on space variables). For the sake of completeness, we announce our results in a setting which allows domains with periodic perforations that may or may not be equal to the whole space $\mathbb {R}^N.$References
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Additional Information
- Mohammad El Smaily
- Affiliation: Department of Mathematical Sciences and Center for Nonlinear Analysis, Carnegie Mellon University, Wean Hall, 5000 Forbes Avenue, Pittsburgh, Pennsylvania 15213 — and — Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais 1049-001 Lisboa, Portugal
- Address at time of publication: Department of Mathematics, University of Toronto, 40 St. George Street, Room 6290, Toronto, ON, M5S 2E4, Canada
- Email: elsmaily@math.toronto.edu
- Received by editor(s): February 28, 2011
- Received by editor(s) in revised form: March 9, 2011, November 11, 2011, and January 3, 2012
- Published electronically: June 26, 2013
- Additional Notes: The author is indebted to the Center for Nonlinear Analysis and Portugal’s Foundation for Science and Technology, “Fundação para a Ciência e a Tecnologia”, for financial and scientific support via the Carnegie Mellon-Portugal Program.
- Communicated by: James E. Colliander
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 3553-3563
- MSC (2010): Primary 35K57, 92D25, 92D40, 35P15, 35P20, 76F10
- DOI: https://doi.org/10.1090/S0002-9939-2013-11728-4
- MathSciNet review: 3080177