12 citations · 12 across the 14 of their papers we have counts for
15 papers
Remarks on temperature-dependent Cahn--Hilliard equations
Mi-Ho Giga, Yoshikazu Giga, Naoto Kajiwara +1
We recall several derivations of temperature-dependent Cahn-Hilliard equations. The resulting equations are systems of mixed order. For a suitable subclass of equations we discuss…
Solutions to a One-Dimensional Combustion-Type Free Boundary Problem via Maximal Regularity
Ken Furukawa, Yoshikazu Giga, Naoto Kajiwara
We study a one-dimensional free boundary problem arising in combustion theory, where the motion of the interface is governed by a prescribed Neumann boundary flux and a zero Dirich…
On dynamic stability of energetically stable equilibria of the Navier-Stokes-Korteweg flows
Yoshikazu Giga, Naoto Kajiwara, Kazuyuki Tsuda
We consider the Navier-Stokes-Korteweg equations in a bounded domain or a periodic cell. The pressure considered in this paper may not be monotone with respect to the density so th…
On existence of a collapsed bubble with surface tension in viscous incompressible fluid
Yoshikazu Giga, Zhongyang Gu
We consider the one-phase free boundary problem for the incompressible Navier-Stokes equations in (). The surface tension is taken into account. The initial d…
Segmentation of monotone data by Kobayashi-Warren-Carter type total variation energies
Yoshikazu Giga, Ayato Kubo, Hirotoshi Kuroda +1
We consider a Kobayashi-Warren-Carter (KWC) type total variation energy with a fidelity term. Since the energy is non-convex, the profiles of minimizers are quite different from th…
Asymptotically self-similar graph-like solutions to a multi-dimensional surface diffusion flow equation under contact angle and no-flux boundary conditions
Yoshikazu Giga, Sho Katayama
This paper studies Mullins' model of thermal grooving which consists of a surface diffusion flow equation with contact angle and no-flux boundary conditions. We consider this probl…
Mosco convergence framework for singular limits of gradient flows on Hilbert spaces with applications
Yoshikazu Giga, Michał Łasica, Piotr Rybka
We consider the question of convergence of a sequence of gradient flows defined on different Hilbert spaces. In order to give meaning to this idea, we introduce a notion of connect…
Remarks on graph-like forward self-similar solutions to the surface diffusion flow equations
Yoshikazu Giga, Sho Katayama
We clarify existence and non-existence of graph-like forward self-similar solutions to the planar surface diffusion equations.
On periodic traveling wave solutions with or without phase transition to the Navier-Stokes-Korteweg and the Euler-Korteweg equations
Yoshikazu Giga, Takahito Kashiwabara, Haruki Takemura
The Navier-Stokes-Korteweg and the Euler-Korteweg equations are considered in isothermal setting. These are diffuse interface models of two-phase flow. For the Navier-Stokes-Kortew…
Large time behavior of exponential surface diffusion flows on
Yoshikazu Giga, Michael Gösswein, Sho Katayama
We consider a surface diffusion flow of the form with a strictly increasing smooth function typically, , for a curve with arc-length parameter $…
No formulation of a new phase for a free boundary problem in combustion theory
Ken Furukawa, Yoshikazu Giga, Naoto Kajiwara
We consider a free boundary problem for the heat equation with a given non-negative external heat source. On the free boundary, we impose the zero Dirichlet condition and the fixed…
On segmentation by total variation type energies of Kobayashi-Warren-Carter type with fidelity
Yoshikazu Giga, Ayato Kubo, Hirotoshi Kuroda +2
We consider a total variation type energy which measures the jump discontinuities different from usual total variation energy. Such a type of energy is obtained as a singular limit…
On a dryout point for a stationary incompressible thermal fluid with phase transition in a pipe
Yoshikazu Giga, Zhongyang Gu
A dryout point is recognized as the position where the phase transition from liquid to vapor occurs. In the one-dimensional case, by solving the stationary incompressible Navier-St…
A few topics on total variation flows
Yoshikazu Giga, Hirotoshi Kuroda, Michał Łasica
Total variation gradient flows are important in several applied fields, including image analysis and materials science. In this paper, we review a few basic topics including defini…
The Primitive Equations in the scaling invariant space
Yoshikazu Giga, Mathis Gries, Matthias Hieber +2
Consider the primitive equations on with initial data of the form , where and $a_2 \in L^\infty_σ(\R^2;L^1(…