1 citations · 1 across the 5 of their papers we have counts for
6 papers
Revisiting the Rellich inequality
Neal Bez, Shuji Machihara, Tohru Ozawa
We revisit the Rellich inequality from the viewpoint of isolating the contributions from radial and spherical derivatives. This naturally leads to a comparison of the norms of the…
Blow-up solutions for non-scale-invariant nonlinear Schrödinger equation in one dimension
Masaru Hamano, Masahiro Ikeda, Shuji Machihara
In this paper, we consider the mass-critical nonlinear Schrödinger equation in one dimension. Ogawa--Tsutsumi [19] proved a blow-up result for negative energy solution by using a s…
Non-delay limit in the energy space from the nonlinear damped wave equation to the nonlinear heat equation
Takahisa Inui, Shuji Machihara
We consider a singular limit problem from the damped wave equation with a power type nonlinearity to the corresponding heat equation. We call our singular limit problem non-delay l…
Blowup solutions for the nonlinear Schrödinger equation with complex coefficient
Shota Kawakami, Shuji Machihara
We construct a finite time blow up solution for the nonlinear Schrödinger equation with the power nonlinearity whose coefficient is complex number. We generalize the range of both…
A supersolutions perspective on hypercontractivity
Yosuke Aoki, Jonathan Bennett, Neal Bez +3
The purpose of this article is to expose an algebraic closure property of supersolutions to certain diffusion equations. This closure property quickly gives rise to a monotone quan…
Sharp ill-posedness of the Dirac-Klein-Gordon system in one dimension
Shuji Machihara, Mamoru Okamoto
We show the ill-posedness of the Cauchy problem for the Dirac-Klein-Gordon system in one dimension in the critical Sobolev space. From this, we finish the classification of the reg…