**Contemporary Mathematics**

Volume: 208;
1997;
350 pp;
Softcover

MSC: Primary 35; 42; 76;

Print ISBN: 978-0-8218-0565-7

Product Code: CONM/208

List Price: $75.00

Individual Member Price: $60.00

**Electronic ISBN: 978-0-8218-7799-9
Product Code: CONM/208.E**

List Price: $75.00

Individual Member Price: $60.00

# Harmonic Analysis and Nonlinear Differential Equations: A Volume in Honor of Victor L. Shapiro

Share this page *Edited by *
*Michel L. Lapidus; Lawrence H. Harper; Adolfo J. Rumbos*

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.

#### Table of Contents

# Table of Contents

## Harmonic Analysis and Nonlinear Differential Equations: A Volume in Honor of Victor L. Shapiro

- Table of Contents vii8 free
- Dedication ix10 free
- Preface xi12 free
- From Reaction-Diffusion to Spherical Harmonics 114 free
- A Survey of Uniqueness Questions in Multiple Trigonometric Series 3548
- A New Look at Some Old Trigonometric Expansions 7386
- Analysis Results and Problems Related to Lattice Points on Surfaces 8598
- A Semilinear Wave Equation with Derivative of Nonlinearity Containing Multiple Eigenvalues of Infinite Multiplicity 111124
- The Structure of the Solutions to Semilinear Equations at a Critical Exponent 133146
- What Do the Navier-Stokes Equations Tell Us about Turbulence? 151164
- A Reminiscence and Survey of Solutions to a JPL Coding Problem 181194
- Weak Limit Sets of Differential Equations 197210
- Towards a Noncommutative Fractal Geometry? Laplacians and Volume Measures on Fractals 211224
- Some Remarks on Global Nonexistence for Nonautonomous Abstract Evolution Equations 253266
- Cartwright and Littlewood on Van der Pol's Equation 265278
- One-Sided Resonance for a Quasilinear Variational Problem 277290
- Shock-Waves in General Relativity 301314
- Dyadic Harmonic Analysis 313326

#### Readership

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.