Publications of the Research Institute for Mathematical Sciences
Online ISSN : 1663-4926
Print ISSN : 0034-5318
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Volume 36, Issue 5
Displaying 1-3 of 3 articles from this issue
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  • Asymptotic Distribution of Eigenfrequencies for Damped Wave Equations
    Johannes Sjöstrand
    2000 Volume 36 Issue 5 Pages 573-611
    Published: 2000
    Released on J-STAGE: April 24, 2009
    DOIhttps://doi.org/10.2977/prims/1195142811
    JOURNAL FREE ACCESS
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    The eigenfrequencies associated to a damped wave equation, are known to belong to a band parallel to the real axis. We establish Weyl asymptotics for the distribution of the real parts of the eigenfrequencies, we show that up to a set of density 0, the eigenfrequencies are confined to a band determined by the Birkhoff limits of the damping coefficient. We also show that certain averages of the imaginary parts converge to the average of the damping coefficient.
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  • On the Approximation of Blow-up Time for Solutions of Nonlinear Parabolic Equations
    Takeo K. Ushijima
    2000 Volume 36 Issue 5 Pages 613-640
    Published: 2000
    Released on J-STAGE: January 22, 2009
    DOIhttps://doi.org/10.2977/prims/1195142812
    JOURNAL FREE ACCESS
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    There are many nonlinear parabolic equations whose solutions develop singularity in finite time, say T. In many cases, a certain norm of the solution tends to infinity as time t approaches T. Such a phenomenon is called blow-up, and T is called the blow-up time. This paper is concerned with approximation of blow-up phenomena in nonlinear parabolic equations. For numerical computations or for other reasons, we often have to deal with approximate equations. But it is usually not at all clear if such wild phenomena as blow-up can be well reflected in the approximate equations. In this paper we present rather simple but general sufficient conditions which guarantee that the blow-up time for the original equation is well approximated by that for approximate equations. We will then apply our result to various examples.
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  • A Rohlin Property for One-parameter Automorphism Groups of the Hyperfinite II1 Factor
    Keiko Kawamuro
    2000 Volume 36 Issue 5 Pages 641-657
    Published: 2000
    Released on J-STAGE: April 24, 2009
    DOIhttps://doi.org/10.2977/prims/1195142813
    JOURNAL FREE ACCESS
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    We first define a Rohlin property for one-parameter automorphism groups of the hyperfinite type II1 factor as an analogue of Kishimoto's definition for one-parameter automorphism groups of unital simple C*-algebras.
    Secondly we prove equivalence between the Rohlin property and the cohomology vanishing in an appropriate central sequence algebra, which is a variation of Kishimoto's theorem in C*-algebra theory.
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