5 citations · 12 across the 7 of their papers we have counts for
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On global existence for semilinear wave equations with spacedependent critical damping
Motohiro Sobajima
The global existence for semilinear wave equations with space-dependent critical damping in an exterior domain is dealt with, wh…
Singular limit problem of abstract second order evolution equations
Ryo Ikehata, Motohiro Sobajima
We consider the singular limit problem in a real Hilbert space for abstract second order evolution equations with a parameter . We first give an alternative…
Rellich inequalities in bounded domains
G. Metafune, L. Negro, M. Sobajima +1
We find necessary and sufficient conditions for the validity of weighted Rellich inequalities in Lp for functions in bounded domains vanishing at the boundary. General operators li…
Global existence of solutions to semilinear damped wave equation with slowly decaying inital data in exterior domain
Motohiro Sobajima
In this paper, we discuss the global existence of weak solutions to the semilinear damped wave equation \begin{equation*} \begin{cases} \partial_t^2u-Δu + \partial_tu = f(u) & \tex…
Finite time blowup of solutions to semilinear wave equation in an exterior domain
Motohiro Sobajima, Kyouhei Wakasa
We consider the initial-boundary value problem of semilinear wave equation with nonlinearity in exterior domain in . Especially, the lifespan of b…
Critical exponent for the semilinear wave equations with a damping increasing in the far field
Kenji Nishihara, Motohiro Sobajima, Yuta Wakasugi
We consider the Cauchy problem of the semilinear wave equation with a damping term \begin{align*} u_{tt} - Δu + c(t,x) u_t = |u|^p, \quad (t,x)\in (0,\infty)\times \mathbb{R}^N,\qu…