arXiv subjects

Hisashi Nishiyama

Publications and source records attributed to Hisashi Nishiyama.

2 recordsLinked to original sources

arXiv2015

Remarks on the asymptotic behavior of the solution of an abstract damped wave equation

We study an abstract damped wave equation. We prove that the solution of the damped wave equation becomes closer to the solution of a heat type equation as time tend to infinity. As an application of our approach, we also study the asymptotic behavior of the damped wave equation in Euclidean space under the geometric control condition.

math.AP↗

arXiv2011

A remark on the Schrödinger equation on Zoll manifolds

On the one dimensional sphere, the support of the fundamental solution to the Schr$\rm \ddot o$dinger equation consists of finite points at the time $t\in 2π\Q$. The paper \cite{Ka} generalized this fact to compact symmetric spaces. In this paper, we consider similar results on Zoll manifolds. We study the singularity for a solution to the equation using a functional calculus of the self-adjoint operator with integer eigenvalues.

math.AP↗