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Recent Advances in Partial Differential Equations, Venice 1996
Edited by: Renato Spigler, University of Padova, Italy, and Stephanos Venakides, Duke University, Durham, NC
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Proceedings of Symposia in Applied Mathematics
1998; 392 pp; hardcover
Volume: 54
ISBN-10: 0-8218-0657-2
ISBN-13: 978-0-8218-0657-9
List Price: US$71
Member Price: US$56.80
Order Code: PSAPM/54
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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.

Readership

Graduate students and research mathematicians interested in ordinary differential equations.

Table of Contents

  • G. I. Barenblatt and A. J. Chorin -- Scaling laws and vanishing viscosity limits in turbulence theory
  • P. Cannarsa and G. Da Prato -- Potential theory in Hilbert spaces
  • C. Cercignani -- Recent developments in the theory of the Boltzmann equation
  • P. Deift, T. Kriecherbauer, and K. T.-R. McLaughlin -- New results for the asymptotics of orthogonal polynomials and related problems via the Lax-Levermore method
  • A. Fannjiang, L. Ryzhik, and G. Papanicolaou -- Evolution of trajectory correlations in steady random flows
  • A. S. Fokas -- Integrability: From d'Alembert to Lax
  • G. Gallavotti -- Methods in the theory of quasi periodic motions
  • S. Klainerman -- Fourier analysis and nonlinear wave equations
  • C. D. Levermore -- The KdV zero-dispersion limit and densities of Dirichlet spectra
  • P.-L. Lions -- On Boltzmann equation and its applications
  • A. J. Majda -- Simplified asymptotic equations for slender vortex filaments
  • D. W. McLaughlin and J. Shatah -- Homoclinic orbits for pde's
  • U. Mosco -- Lagrangian metrics on fractals
  • E. Tadmor -- Approximate solutions of nonlinear conservation laws and related equations
  • S. Venakides -- The small dispersion KdV equation with decaying initial data
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