Zobrazeno 1 - 10
of 143
pro vyhledávání: '"Sobajima, Motohiro"'
Autor:
Sobajima, Motohiro
In this paper, we mainly discuss asymptotic profiles of solutions to a class of abstract second-order evolution equations of the form $u''+Au+u'=0$ in real Hilbert spaces, where $A$ is a nonnegative selfadjoint operator. The main result is the asympt
Externí odkaz:
http://arxiv.org/abs/2410.19366
Autor:
Metafune, Giorgio, Sobajima, Motohiro
We characterize the domain of the Schr\"odinger operators $S=-\Delta+c|x|^{-\alpha}$ in $L^p(\mathbb{R}^N)$, with $0<\alpha<2$ and $c\in\mathbb{R}$. When $\alpha p< N$, the domain characterization is essentially known and can be proved using differen
Externí odkaz:
http://arxiv.org/abs/2409.09917
Autor:
Sobajima, Motohiro
The optimality of decay properties of the one-dimensional damped wave equations with potentials belonging to a certain class is discussed. The typical ingredient is a variant of Nash inequality which involves an invariant measure for the correspondin
Externí odkaz:
http://arxiv.org/abs/2308.15680
Lifespan estimates for semilinear damped wave equations of the form $\partial_t^2u-\Delta u+\partial_tu=|u|^p$ in a two dimensional exterior domain endowed with the Dirichlet boundary condition are dealt with. For the critical case of the semilinear
Externí odkaz:
http://arxiv.org/abs/2305.05124
Autor:
Sobajima, Motohiro
Publikováno v:
In Journal of Mathematical Analysis and Applications 1 February 2025 542(1)
Autor:
Sobajima, Motohiro, Wakasugi, Yuta
We study the large time behavior of solutions to the wave equation with space-dependent damping in an exterior domain. We show that if the damping is effective, then the solution is asymptotically expanded in terms of solutions of corresponding parab
Externí odkaz:
http://arxiv.org/abs/2203.06360
Autor:
Sobajima, Motohiro
The global existence for semilinear wave equations with space-dependent critical damping $\partial_t^2u-\Delta u+\frac{V_0}{|x|}\partial_t u=f(u)$ in an exterior domain is dealt with, where $f(u)=|u|^{p-1}u$ and $f(u)=|u|^p$ are in mind. Existence an
Externí odkaz:
http://arxiv.org/abs/2106.06107
Akademický článek
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Akademický článek
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Autor:
Miyazaki, Hayato, Sobajima, Motohiro
Publikováno v:
Advances in Harmonic Analysis and Partial Differential Equations (2020), pp. 197-207
This paper is concerned with the upper bound of the lifespan of solutions to nonlinear Schr\"odinger equations with general homogeneous nonlinearity of the critical order. In [8], Masaki and the first author obtain the upper bound of the lifespan of
Externí odkaz:
http://arxiv.org/abs/1912.12794