Soichiro Katayama
The energy decay and asymptotics for a class of semilinear wave equations in two space dimensions.
Пнд, 11/21/2011 - 15:01 — SomNambulAuthors: Soichiro Katayama, Daisuke Murotani, Hideaki Sunagawa
Subjects: Analysis of PDEs
AbstractWe consider semilinear wave equations with small initial data in two space
dimensions. For a class of wave equations with cubic nonlinearity, we show the
global existence of small amplitude solutions, and give an asymptotic
description of the solution as $t \to \infty$ uniformly in $x \in {\mathbb
R}^2$. In particular, our result implies the decay of the energy when the
nonlinearity is dissipative.Lower bound of the lifespan of solutions to semilinear wave equations in an exterior domain.
Ср, 09/08/2010 - 15:01 — SomNambulAuthors: Soichiro Katayama, Hideo Kubo
Subjects: Analysis of PDEs
AbstractWe consider the Cauchy-Dirichlet problem for semilinear wave equations in a
three space dimensional domain exterior to a bounded and non-trapping obstacle.
We obtain a detailed estimate for the lower bound of the lifespan of classical
solutions when the size of initial data tends to zero, in a similar spirit to
that of the works of John and H\"ormander where the Cauchy problem was treated.
We show that our estimate is sharp at least for some special case.Decay estimates of a tangential derivative to the light cone for the wave equation and their application.
Пнд, 08/31/2009 - 17:16 — SomNambulAuthors: Soichiro Katayama, Hideo Kubo
Subjects: Analysis of PDEs
AbstractWe consider wave equations in three space dimensions, and obtain new weighted
$L^\infty$-$L^\infty$ estimates for a tangential derivative to the light cone.
As an application, we give a new proof of the global existence theorem, which
was originally proved by Klainerman and Christodoulou, for systems of nonlinear
wave equations under the null condition. Our new proof has the advantage of
using neither the scaling nor the pseudo-rotation operators.Global existence for coupled systems of nonlinear wave and Klein-Gordon equations in three space dimensions.
Пнд, 08/31/2009 - 17:16 — SomNambulAuthors: Soichiro Katayama
Subjects: Analysis of PDEs
AbstractWe consider the Cauchy problem for coupled systems of wave and Klein-Gordon
equations with quadratic nonlinearity in three space dimensions. We show global
existence of small amplitude solutions under certain condition including the
null condition on self-interactions between wave equations. Our condition is
much weaker than the strong null condition introduced by Georgiev for this kind
of coupled system. Consequently our result is applicable to certain physical
systems, such as the Dirac-Klein-Gordon equations, the Dirac-Proca equations,
and the Klein-Gordon-Zakharov equations.
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