33 citations · 119 across the 43 of their papers we have counts for
43 papers · 1 filter
On existence and uniqueness for transport equations with non-smooth velocity fields under inhomogeneous Dirichlet data
Tokuhiro Eto, Yoshikazu Giga
A transport equation with a non-smooth velocity field is considered under inhomogeneous Dirichlet boundary conditions. The spatial gradient of the velocity field is assumed in $L^{…
A convergence result for a minimizing movement scheme for mean curvature flow with prescribed contact angle in a curved domain
Tokuhiro Eto, Yoshikazu Giga
We consider a minimizing movement scheme of Chambolle type for the mean curvature flow equation with prescribed contact angle condition in a smooth bounded domain in …
The three limits of the hydrostatic approximation
Ken Furukawa, Yoshikazu Giga, Matthias Hieber +3
The primitive equations are derived from the -Navier-Stokes equations by the hydrostatic approximation. Formally, assuming an -thin domain and anisotropic viscosit…
On a diffusion equation with rupture
Yoshikazu Giga, Yuki Ueda
We propose a model to describe an evolution of a bubble cluster with rupture. In a special case, the equation is reduced to a single parabolic equation with evaporation for the thi…
The Helmholtz decomposition of a type vector field in general unbounded domains
Yoshikazu Giga, Zhongyang Gu
We consider a space of vector fields with bounded mean oscillation whose ``normal'' component to the boundary is well-controlled. In the case when the dimension , w…
Fractional time differential equations as a singular limit of the Kobayashi-Warren-Carter system
Yoshikazu Giga, Ayato Kubo, Hirotoshi Kuroda +3
This paper is concerned with a singular limit of the Kobayashi-Warren-Carter system, a phase field system modelling the evolutions of structures of grains. Under a suitable scaling…
A level-set method for a mean curvature flow with a prescribed boundary
Xingzhi Bian, Yoshikazu Giga, Hiroyoshi Mitake
We propose a level-set method for a mean curvature flow whose boundary is prescribed by interpreting the boundary as an obstacle. Since the corresponding obstacle problem is global…
The Helmholtz decomposition of a type vector field in a slightly perturbed half space
Yoshikazu Giga, Zhongyang Gu
We introduce a space of vector fields with bounded mean oscillation whose normal component to the boundary is well-controlled. We establish its Helmholtz decomposition in the…
The heat equation with the dynamic boundary condition as a singular limit of problems degenerating at the boundary
Yoshikazu Giga, Michał Łasica, Piotr Rybka
We derive the dynamic boundary condition for the heat equation as a limit of boundary layer problems. We study convergence of their weak and strong solutions as the width of the la…
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 fourth-order total variation flow in
Yoshikazu Giga, Hirotoshi Kuroda, Michał Łasica
We define rigorously a solution to the fourth-order total variation flow equation in . If , it can be understood as a gradient flow of the total variation ene…
Exhaustive existence and non-existence results for Hardy-Hénon equations in
Yoshikazu Giga, Quôc Anh Ngô
This paper concerns solutions to the Hardy-Hénon equation \[ -Δu = |x|^σu^p \] in with and arbitrary . This equation was proposed by Hé…
Motion by crystalline-like mean curvature: a survey
Yoshikazu Giga, Norbert Požár
We consider a class of anisotropic curvature flows called a crystalline curvature flow. We present a survey on this class of flows with special emphasis on the well-posedness of it…
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…
Continuity of derivatives of a convex solution to a perturbed one-Laplace equation by -Laplacian
Yoshikazu Giga, Shuntaro Tsubouchi
We consider a one-Laplace equation perturbed by -Laplacian with . We prove that a weak solution is continuously differentiable () if it is convex. Note that s…
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,…
A finer singular limit of a single-well Modica--Mortola functional and its applications to the Kobayashi--Warren--Carter energy
Yoshikazu Giga, Jun Okamoto, Masaaki Uesaka
An explicit representation of the Gamma limit of a single-well Modica--Mortola functional is given for one-dimensional space under the graph convergence which is finer than convent…
Remarks on large time behavior of level-set mean curvature flow equations with driving and source terms
Yoshikazu Giga, Hiroyoshi Mitake, Hung V. Tran
We study a level-set mean curvature flow equation with driving and source terms, and establish convergence results on the asymptotic behavior of solutions as time goes to infinity…
A new numerical scheme for constrained total variation flows and its convergence
Yoshikazu Giga, Koya Sakakibara, Kazutoshi Taguchi +1
In this paper, we propose a new numerical scheme for a spatially discrete model of constrained total variation flows, which are total variation flows whose values are constrained i…
On a discrete scheme for time fractional fully nonlinear evolution equations
Yoshikazu Giga, Qing Liu, Hiroyoshi Mitake
We introduce a discrete scheme for second order fully nonlinear parabolic PDEs with Caputo's time fractional derivatives. We prove the convergence of the scheme in the framework of…
On boundary detachment phenomena for the total variation flow with dynamic boundary conditions
Yoshikazu Giga, Ryota Nakayashiki, Piotr Rybka +1
We combine the total variation flow suitable for crystal modeling and image analysis with the dynamic boundary conditions. We analyze the behavior of facets at the parts of the bou…