Functional-analytic methods for partial differential equations : proceedings of a conference and a symposium held in Tokyo, Japan, July 3-9, 1989

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Functional-analytic methods for partial differential equations : proceedings of a conference and a symposium held in Tokyo, Japan, July 3-9, 1989

H. Fujita, T. Ikebe, S.T. Kuroda (eds.)

（Lecture notes in mathematics, 1450）

Springer-Verlag, c1990

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Proceedings of the International Conference on Functional Analysis and Its Application in Honor of Professor Tosio Kato, July 3-6, 1989, University of Tokyo, and the Symposium on Spectral and Scattering Theory, held July 7-9, 1989, at Gakushuin University, Tokyo

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Description and Table of Contents

Description

In these meetings, which were held in honour of Professor Tosio Kato on his retirement, the focus was on the interplay of functional analysis and partial differential equations. Thus, the study of Schrodinger operators, from the viewpoints of evolution equations and spectral theory, is one major subject, while functional analytic studies of nonlinear PDEs, including Navier-Stokes, KdV and other equations, constitutes another main theme. Papers on these linear and nonlinear problems are linked through their methods and types of approach.

Table of Contents

Spectral concentration for dense point spectrum.- Behaviour of a semilinear periodic-parabolic problem when a parameter is small.- On smoothing property of Schroedinger propagators.- A coin tossing problem of R. L. Rivest.- Liapunov functions and monotonicity in the Navier-Stokes equation.- Singular solutions of a nonlinear elliptic equation and an infinite dimensional dynamical system.- to geometric potential theory.- KDV, BO and friends in weighted Sobolev spaces.- The square root problem for elliptic operators a survey.- The initial value problem for a class of nonlinear dispersive equations.- On Schroedinger operators with magnetic fields.- Existence of bound states for double well potentials and the Efimov effect.- High energy asymptotics for the total scattering phase in potential scattering theory.- Feynman path integral to relativistic quantum mechanics.- On the distribution of poles of the scattering matrix for several convex bodies.- Smoothing effect for the Schroedinger evolution equations with electric fields.- Blow-up of solutions for the nonlinear Schroedinger equation with quartic potential and periodic boundary condition.

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