Hideo Kubo
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.
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