2 citations · 7 across the 14 of their papers we have counts for
19 papers · 1 filter
Graph gradient flows : from discrete to continuum
Yoshikazu Giga, Yves van Gennip, Jun Okamoto
This paper gives a framework to study a continuum limit of a gradient flow on a graph where the number of vertices increases in an appropriate way. As examples we prove the converg…
On a singular limit of the Kobayashi--Warren--Carter energy
Yoshikazu Giga, Jun Okamoto, Koya Sakakibara +1
By introducing a new topology, a representation formula of the Gamma limit of the Kobayashi-Warren-Carter energy is given in a multi-dimensional domain. A key step is to study the…
The Helmholtz decomposition of a space of vector fields with bounded mean oscillation in a bounded domain
Yoshikazu Giga, Zhongyang Gu
We introduce a space of vector fields with bounded mean oscillation whose ``tangential'' and ``normal'' components to the boundary behave differently. We establish its Helmholtz de…
On the equivalence of viscosity solutions and distributional solutions for the time-fractional diffusion equation
Yoshikazu Giga, Hiroyoshi Mitake, Shoichi Sato
We consider an initial-boundary value problem for the time-fractional diffusion equation. We prove the equivalence of two notions of weak solutions, viscosity solutions and distrib…
Viscosity solutions for the crystalline mean curvature flow with a nonuniform driving force term
Yoshikazu Giga, Norbert Pozar
A general purely crystalline mean curvature flow equation with a nonuniform driving force term is considered. The unique existence of a level set flow is established when the drivi…
The Hydrostatic Approximation for the Primitive Equations by the Scaled Navier-Stokes Equations under the No-Slip Boundary Condition
Ken Furukawa, Yoshikazu Giga, Takahito Kashiwabara
In this paper we justify the hydrostatic approximation of the primitive equations in the maximal --setting in the three-dimensional layer domain $Ω= \Torus^2 \times (-1,…