7 papers · 1 filter
Subcriticality of subordinated Schrödinger operators and their application to wave equations
Takumu Ooi, Motohiro Sobajima
We provide a probabilistic characterization of criticality, subcriticality, and supercriticality for subordinated Schrödinger operators. We also investigate the relationship betwe…
Threshold for the existence of scattering states for nonlinear Schrödinger equations without gauge invariance
Hayato Miyazaki, Motohiro Sobajima
This paper is concerned with a threshold phenomenon for the existence of scattering states for nonlinear Schrödinger equations. The nonlinearity includes a non-oscillatory term of…
Remarks on criticality theory for Schrödinger operators and its application to wave equations with potentials
Motohiro Sobajima
In this paper, we give an alternative perspective of the criticality theory for (nonnegative) Schrödinger operators. Schrödinger operator is classified as subcritical/c…
On the decay of mass with respect to an invariant measure for semilinear heat equations in exterior domains
Ahmad Fino, Motohiro Sobajima
The paper concerns with the decay property of solutions to the initial-boundary value problem of the semilinear heat equation in exterior domains in $\…
The critical Fujita exponent for one-dimensional semilinear heat equations with potentials and space-dependent nonlinearities
Reiri Miyamoto, Motohiro Sobajima
This paper is concerned with the existence/nonexistence of nontrivial global-in-time solutions to the Cauchy problem \begin{equation} \begin{cases}\tag{P}\partial_tu-\partial_x^2u+…
Appearance of Strauss-type exponent in semilinear wave equations with time-dependent speed of propagation
Motohiro Sobajima, Kimitoshi Tsutaya, Yuta Wakasugi
In this paper, blowup phenomenon for the semilinear wave equation with time-dependent speed of propagation and scattering damping is considered under the smallness of initial data.…