Contemporary Mathematics 1997; 350 pp; softcover Volume: 208 ISBN10: 0821805657 ISBN13: 9780821805657 List Price: US$71 Member Price: US$56.80 Order Code: CONM/208
 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. 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. Table of Contents  V. L. Shapiro  From reactiondiffusion 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 NavierStokes 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  Onesided resonance for a quasilinear variational problem
 J. A. Smoller and J. B. Temple  Shockwaves in general relativity
 W. R. Wade  Dyadic harmonic analysis
