2 citations · 3 across the 9 of their papers we have counts for
10 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…
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…
Solution formula for generalized two-phase Stokes equations and its applications to maximal regularity; model problems
Naoto Kajiwara
In this paper we give a solution formula for the two-phase Stokes equations with and without surface tension and gravity in the whole space with flat interface. The solution formul…
Maximal - regularity for the Stokes equations with various boundary conditions in the half space
Naoto Kajiwara
We prove resolvent estimates and maximal - regularity estimates for the Stokes equations with Dirichlet, Neumann and Robin boundary conditions in the half space. Ea…
Higher regularity for parabolic equations based on maximal L_p-L_q spaces
Naoto Kajiwara
In this paper we prove higher regularity for 2m-th order parabolic equations with general boundary conditions. This is a kind of maximal L_p-L_q regularity with differentiability,…
Strong time-periodic solutions to the bidomain equations with arbitrary large forces
Yoshikazu Giga, Naoto Kajiwara, Klaus Kress
We prove the existence of strong time-periodic solutions to the bidomain equations with arbitrary large forces. We construct weak time-periodic solutions by a Galerkin method combi…
Strong Time Periodic Solutions to the Bidomain Equations with FitzHugh-Nagumo Type Nonlinearities
Matthias Hieber, Naoto Kajiwara, Klaus Kress +1
Consider the bidomain equations subject to ionic transport described by the models of FitzHugh-Nagumo, Aliev-Panfilov, or Rogers-McCulloch. It is proved that this set of equations…
On a resolvent estimate for bidomain operators and its applications
Yoshikazu Giga, Naoto Kajiwara
We study bidomain equations that are commonly used as a model to represent the electrophysiological wave propagation in the heart. We prove existence, uniqueness and regularity of…