Research Page
Topics in Strong Localized Perturbation Theory
description to be written; pictures
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Strong Localized Perturbations of Eigenvalue Problems
with J.B. Keller
(SIAM J. Appl. Math., Vol. 53, No. 3, (1993), pp. 770-798.)
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Summing Logarithmic Expansions for Singularly Perturbed Eigenvalue
Problems
with W.D. Henshaw, J.B. Keller
(SIAM J. Appl. Math., Vol. 53, No. 3, (1993), pp. 799-828.)
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Asymptotics Beyond All Orders for a Low Reynolds Number Flow
with J.B. Keller (J. Engineering Mathematics, Vol. 30, (1996) pp.
253-265.)
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An Asymptoptic Study of Oxygen Transport from Multiple Capillaries to
Skeletal Muscle Tissue
with M. Titcombe (SIAM J. Appl. Math., Vol. 60, No. 5, (2000),
pp. 1767-1788.)
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Summing Logarithmic Expansions for Elliptic Equations in
Multiply-Connected Domains with Small Holes
with M. Titcombe (Canadian Quart. Appl. Math., Vol. 7, No. 3,
(1999), pp. 313-343.)
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Diffusion and Bifurcation Problems in Singularly Perturbed Domains
Equations
(Natural Resource Modeling, Vol. 13, No. 2, (2000), pp. 271-302.)
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Asymptotic Methods for PDE Problems in Fluid Mechanics and Related
Systems with Strong Localized Perturbations in Two-Dimensional Domains
with M.C. Kropinski (book chapter in
"Asymptotic Methods in Fluid Mechanics: Surveys and Results",
CISM International Centre for Mechanical Science, Vol. 523, (2010), Springer
48 pages.) Some
- Problems to accompany
the notes.
- Transition to Point Constraint
in a Mixed Biharmonic Eigenvalue Problem
with A. Lindsay and T. Kolokolnikov (SIAM J. Appl. Math., Vol. 75
No. 3, (2015), pp. 1193-1224).
- A Hybrid
Asymptotic-Numerical Method for Calculating Drag Coefficients in 2-D
Low Reynolds Number Flow
with S. Hormozi, (J. Eng. Math., Vol. 102 No. 1, (2017),
pp. 3-33).
- Spots, Traps, and Patches: Asymptotic
Analysis of Localized Solutions to some Linear and Nonlinear Diffusive
Systems,
(Nonlinearity, Vol. 31, No. 8, (2018), R189).