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Harmonic Analysis and Nonlinear Differential Equations: A Volume in Honor of Victor L. Shapiro
Edited by: Michel L. Lapidus and Lawrence H. Harper, University of California, Riverside, CA, and Adolfo J. Rumbos, Pomona College, Claremont, CA

Contemporary Mathematics
1997; 350 pp; softcover
Volume: 208
ISBN-10: 0-8218-0565-7
ISBN-13: 978-0-8218-0565-7
List Price: US$75
Member Price: US$60
Order Code: CONM/208
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This volume is a collection of papers dealing with harmonic analysis and nonlinear differential equations and stems from a conference on these two areas and their interface held in November 1995 at the University of California, Riverside, in honor of V. L. Shapiro. There are four papers dealing directly with the use of harmonic analysis techniques to solve challenging problems in nonlinear partial differential equations. There are also several survey articles on recent developments in multiple trigonometric series, dyadic harmonic analysis, special functions, analysis on fractals, and shock waves, as well as papers with new results in nonlinear differential equations. These survey articles, along with several of the research articles, cover a wide variety of applications such as turbulence, general relativity and black holes, neural networks, and diffusion and wave propagation in porous media. A number of the papers contain open problems in their respective areas.


Graduate students and research mathematicians interested in recent developments in harmonic analysis and nonlinear partial differential equations; researchers interested in black holes, turbulence, multiple trigonometric series, dyadic harmonic analysis, and analysis on fractals; physicists and engineers.

Table of Contents

  • V. L. Shapiro -- From reaction-diffusion to spherical harmonics
  • J. M. Ash and G. Wang -- A survey of uniqueness questions in multiple trigonometric series
  • R. Askey -- A new look at some old trigonometric expansions
  • J. Bourgain -- Analysis results and problems related to lattice points on surfaces
  • J. F. Caicedo and A. Castro -- A semilinear wave equation with derivative of nonlinearity containing multiple eigenvalues of infinite multiplicity
  • A. L. Edelson -- The structure of the solutions to semilinear equations at a critical exponent
  • C. Foias -- What do the Navier-Stokes equations tell us about turbulence?
  • L. H. Harper -- A reminiscence and survey of solutions to a JPL coding problem
  • M. W. Hirsch -- Weak limit sets of differential equations
  • M. L. Lapidus -- Towards a noncommutative fractal geometry? Laplacians and volume measures on fractals
  • H. A. Levine, P. Pucci, and J. Serrin -- Some remarks on global nonexistence for nonautonomous abstract evolution equations
  • S. L. McMurran and J. J. Tattersall -- Cartwright and Littlewood on Van der Pol's equation
  • A. J. Rumbos and V. L. Shapiro -- One-sided resonance for a quasilinear variational problem
  • J. A. Smoller and J. B. Temple -- Shock-waves in general relativity
  • W. R. Wade -- Dyadic harmonic analysis
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