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CANARDS IN ADVECTION–REACTION–DIFFUSION SYSTEMS IN ONE SPATIAL DIMENSION

Part of: General theory in ordinary differential equations Asymptotic theory Qualitative theory Representations of solutions Physiological, cellular and medical topics

Published online by Cambridge University Press:  16 June 2015

KRISTEN HARLEY
KRISTEN HARLEY*
Affiliation:
Mathematical Sciences School, Queensland University of Technology, Brisbane, Australia email kristen.e.harley@gmail.com
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Abstract

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Keywords

advection–reaction–diffusion systemstravelling wave solutionsgeometric singular perturbation theorycanards

MSC classification

Primary: 34E17: Canard solutions
Secondary: 34A12: Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions 34C37: Homoclinic and heteroclinic solutions 34E15: Singular perturbations, general theory 35C07: Traveling wave solutions 92C17: Cell movement (chemotaxis, etc.)
Type
Abstracts of Australasian PhD Theses
Information
Bulletin of the Australian Mathematical Society , Volume 92 , Issue 2 , October 2015 , pp. 342 - 343
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

References

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Perumpanani, A. J., Sherratt, J. A., Norbury, J. and Byrne, H. M., ‘A two parameter family of travelling waves with a singular barrier arising from the modelling of extracellular matrix mediated cellular invasion’, Physica D 126(3–4) (1999), 145–159.Google Scholar
Pettet, G. J., McElwain, D. L. S. and Norbury, J., ‘Lotka–Volterra equations with chemotaxis: walls, barriers and travelling waves’, IMA J. Math. Appl. Med. Biol. 17 (2000), 395–413.Google ScholarPubMed