Proceedings of Symposia in Applied Mathematics 1998; 392 pp; hardcover Volume: 54 ISBN10: 0821806572 ISBN13: 9780821806579 List Price: US$71 Member Price: US$56.80 Order Code: PSAPM/54
 Lax and Nirenberg are two of the most distinguished mathematicians of our times. Their work on partial differential equations (PDEs) over the last halfcentury 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 weeklong 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 blowup 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 LaxLevermore 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 zerodispersion 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
