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Fluids and Waves: Recent Trends in Applied Analysis
Edited by: Fernanda Botelho, Thomas Hagen, and James Jamison, University of Memphis, TN
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Contemporary Mathematics
2007; 287 pp; softcover
Volume: 440
ISBN-10: 0-8218-4247-1
ISBN-13: 978-0-8218-4247-8
List Price: US$81
Member Price: US$64.80
Order Code: CONM/440
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This volume contains a series of articles on wave phenomena and fluid dynamics, highlighting recent advances in these two areas of mathematics. The collection is based on lectures presented at the conference "Fluids and Waves--Recent Trends in Applied Analysis" and features a rich spectrum of mathematical techniques in analysis and applications to engineering, neuroscience, physics, and biology. The mathematical topics discussed range from partial differential equations, dynamical systems and stochastic processes, to areas of classical analysis.

This volume is intended as an introduction to major topics of interest and state-of-the-art analytical research in wave motion and fluid flows. It is helpful to junior mathematicians to stay abreast of new techniques and recent trends in these areas of mathematics. The articles here also provide a unique scientific basis for recent results and new links between current research themes. In summary, this book is a guide for experts in one field to the issues of the other, and will challenge graduate students to investigate these areas of analysis in further detail.

Readership

Graduate students and research mathematicians interested in mathematical aspects of fluid dynamics.

Table of Contents

  • K. T. Andrews, S. Anderson, R. S. R. Menike, M. Shillor, R. Swaminathan, and J. Yuzwalk -- Vibrations of a damageable string
  • G. Avalos and R. Triggiani -- The coupled PDE system arising in fluid/structure interaction. Part I: Explicit semigroup generator and its spectral properties
  • V. Barbu, Z. Grujić, I. Lasiecka, and A. Tuffaha -- Existence of the energy-level weak solutions for a nonlinear fluid-structure interaction model
  • A. Biswas and D. Swanson -- Gevrey regularity of solutions to the 3D Navier-Stokes equations
  • P. C. Bressloff -- Stimulus-induced bumps in two-dimensional neural field theory
  • S. N. Chandler-Wilde and M. Lindner -- Wave problems in unbounded domains: Fredholmness and the finite section method
  • S. Coombes and M. R. Owen -- Exotic dynamics in a firing rate model of neural tissue with threshold accommodation
  • M. H. Garzon, D. R. Blain, and M. West -- Embedded models of self-assembly of DNA complexes
  • M. He -- A parameter property of integrodifferential equations with memory
  • J. M. Lavine, E. C. Eckstein, and J. A. Goldstein -- Stochastic models with negative friction for intermittent rolling of biological mimetics
  • J. A. H. Murdock -- Multi-parameter oscillatory connection functions in neural field models
  • N. Popović -- Front speeds, cut-offs, and desingularization: A brief case study
  • J. M. Rodriguez and M. H. Garzon -- Neural networks can learn to approximate autonomous flows
  • C. M. Schober -- Rogue waves, non-Gaussian statistics and proximity to homoclinic data
  • H. Schurz -- Nonlinear stochastic wave equations in \(\mathbb{R}^1\) with power-law nonlinearity and additive space-time noise
  • J. Tolosa -- The method of Lyapunov functions of two variables
  • J. Zhu -- Analysis of map formation in visual perception
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