MATH 551: LOCALIZED PERTURBATION PAPERS
Here is a list of possible papers that you can look at based on strong localized perturbation theory.
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G.R. Bigg, E.O. Tuck, Two-Dimensional Resonators with Small Openings , J. Austral. Math.
Soc. (Series B), 24, (1982), pp. 2-27.
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P. Monkewitz, N. Nguyen-Vo, The Response of Helmholtz Resonators to External Excitation.
Part 1. Single Resonators , J. Fluid. Mech. Vol. 151, (1985), pp. 477-497.
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A. Peirce, H. Rabitz, Effect of Defect Structures on Chemically Active Surfaces: A Continuum
Approach , Physical Rev. B, Vol. 38, No. 3, (1988), pp. 1734-1753.
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A. Friedman, M. Vogelius, Identification of Small Inhomogeneities of Extreme Conductivity by
Boundary Measurments , Arch. Rational Mech. Anal., Vol. 105, Bo. 4, (1989), pp. 299-326.
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E. Beretta, A. Mukherjee, M. Vogelius, Asymptotic Formulas for Steady-State Voltage Potentials in the Presence of Conductivity Imperfections of Small Area , Z. Angew. Math. Phys.
Vol. 52, No. 4, (2001), pp. 543-572.
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J. Arrieta, Rates of Eigenvalues on a Dumbbell Domain. The Simple Eigenvalue Case , Trans.
Amer. Math. Soc. Vol. 347, No. 9, (1995), pp. 3503-3531.
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J. A. P. Aranha, Existence and Some Proprties of Waves Trapped By Submerged Cylinders ,
J. Fluid. Mech. Vol. 192, (1988), pp. 421-433.
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M. C. Kropinski, M. J. Ward, J. B. Keller, A Hybrid Asymptotic-Numerical Method for
Calculating Low Reynolds Number Flows Past Symmetric Cylindrical Bodies , SIAM J. Appl.
Math. Vol. 55. No. 6, (1995), pp. 1484-1510.
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M. Titcombe, M. J. Ward, An Asymptotic Study of Oxygen Transport from Multiple Capillaries to Skeletal Muscle Tissue , SIAM J. Appl. Math. Vol. 60, No. 5, (2000), pp. 1767-1788.
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M. C. Kropinski, A. Lindsay, M. J. Ward, Asymptotic Analysis of Localized Solutions to Some
Linear and Nonlinear Biharmonic Eigenvalue Problems , Studies in App. Math., Vol. 126 No.
4, (2011), pp. 347–408.
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A. Lindsay, M. J. Ward, An Asymptotic Analysis of the Persistence Threshold in Highly
Patchy Spatial Environments , Discrete and Continuous Dynamical Systems, Series B, Vol.
14, No. 3., (2010), pp. 1139–1179.
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S. Pillay, M. J. Ward, A. Pierce, T. Kolokolnikov, An Asymptotic Analysis of the Mean
First Passage Time for Narrow Escape Problems: Part I: Two-Dimensional Domains , SIAM
Multiscale Modeling and Simulation, Vol. 8, No. 3, (2010), pp. 803–835.
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T. Kolokolnikov, M. Titcombe, M. J. Ward, Optimizing the Fundamental Neumann Eigenvalue for the Laplacian in a Domain with Small Traps , European J. Appl. Math., Vol. 16,
No. 2, (2005), pp. 161–200.
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R. Straube, M. J. Ward, Intraceulluar Signalling Gradients Arising from Multiple Compartments: A Matched Asymptotic Expansion Approach , SIAM J. Appl. Math, Vol. 70, No. 1,
(2009), pp. 248–269.
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D. Coombs, R. Straube, M. J. Ward, Diffusion on a Sphere with Localized Traps: Mean First
Passage Time, Eigenvalue Asymptotics, and Fekete Points , SIAM J. Appl. Math., Vol. 70,
No. 1, (2009), pp. 302–332.
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C. Levy, D. Iron, Dynamics and Stability of a Three-Dimensional Model of Cell Signal Transduction , J. Math. Biology, October 2012 (online first).
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A. Cheviakov, M. J. Ward, R. Straube, An Asymptotic Analysis of the Mean First Passage
Time for Narrow Escape Problems: Part II: The Sphere , SIAM Multiscale Modeling and
Simulation, Vol. 8, No. 3, (2010), pp. 836–870.
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N. Alikakos, G. Fusco, The Equations of Ostwald Ripening for Dilute Systems , J. Statist.
Phys. Vol. 95, No. 5-6, (1999), pp. 851-866.
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N. Alikakos, G. Fusco, G. Karali, Ostwald Ripening in Two Dimensions: The Rigorous Derivation of the Equations from the Mullins-Sekerka Dynamics , Journal of Differential Equations,
205 (1), (2004), pp. 1–49.
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P. Voorhees, The Theory of Ostwald Ripening , J. Statis. Phys. Vol. 38, No. 1-2, (1985), pp.
231-252.
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