**Proceedings of Symposia in Applied Mathematics**

Volume: 54;
1998;
392 pp;
Hardcover

MSC: Primary 34; 35; 42; 60; 65; 70; 76;

Print ISBN: 978-0-8218-0657-9

Product Code: PSAPM/54

List Price: $75.00

Individual Member Price: $60.00

**Electronic ISBN: 978-0-8218-9269-5
Product Code: PSAPM/54.E**

List Price: $75.00

Individual Member Price: $60.00

# Recent Advances in Partial Differential Equations, Venice 1996

Share this page *Edited by *
*Renato Spigler; Stephanos Venakides*

Lax and Nirenberg are two of the most distinguished mathematicians of our
times. Their work on partial differential equations (PDEs) over the last
half-century has dramatically advanced the subject and has profoundly
influenced the course of mathematics. A huge part of the development in PDEs
during this period has either been through their work, motivated by it or
achieved by their postdocs and students.

A large number of mathematicians honored these two exceptional scientists in a
week-long conference in Venice (June 1996) on the occasion of their 70th
birthdays.

This volume contains the proceedings of the conference, which focused on the
modern theory of nonlinear PDEs and their applications. Among the topics
treated are turbulence, kinetic models of a rarefied gas, vortex filaments,
dispersive waves, singular limits and blow-up of solutions, conservation laws,
Hamiltonian systems, and others. The conference served as a forum for the
dissemination of new scientific ideas and discoveries and enhanced scientific
communication by bringing together such a large number of scientists working in
related fields. The event allowed the international mathematics community to
honor two of its outstanding members.

#### Table of Contents

# Table of Contents

## Recent Advances in Partial Differential Equations, Venice 1996

- Contents vii8 free
- Preface ix10 free
- List of funding institutions and other sponsors xi12 free
- Scaling laws and vanishing viscosity limits in turbulence theory 114 free
- Potential theory in Hilbert spaces 2740
- Recent developments in the theory of the Boltzmann equation 5366
- New results for the asymptotics of orthogonal polynomials and related problems via the Lax-Levermore method 87100
- Evolution of trajectory correlations in steady random flows 105118
- Integrability: from d'Alembert to Lax 131144
- Methods in the theory of quasi periodic motions 163176
- Fourier analysis and nonlinear wave equations 175188
- The KdV zero-dispersion limit and densities of Dirichlet spectra 187200
- On Boltzmann equation and its applications 211224
- Simplified asymptotic equations for slender vortex filaments 237250
- Homoclinic orbits for pde's 281294
- Lagrangian metrics on fractals 301314
- Approximate solutions of nonlinear conservation laws and related equations 325338
- The small dispersion KdV equation with decaying initial data 369382

#### Readership

Graduate students and research mathematicians interested in ordinary differential equations.