36 citations · 125 across the 20 of their papers we have counts for
21 papers
Permeability parameter asymptotics in a Cahn--Hilliard system with third type transmission conditions
Pierluigi Colli, Takeshi Fukao, Kei Fong Lam
In this paper, we study a system in which the Cahn--Hilliard system is imposed in the bulk domain and an Allen--Cahn type equation is prescribed on the boundary, connected through…
Asymptotic analysis of the Allen-Cahn equation with dynamic boundary conditions of Cahn-Hilliard type
Pierluigi Colli, Takeshi Fukao
Problems for partial differential equations coupled with dynamic boundary conditions can be viewed as a type of transmission problem between the bulk and its boundary. For the heat…
Heat equation on the hypergraph containing vertices with given data
Takeshi Fukao, Masahiro Ikeda, Shun Uchida
This paper is concerned with the Cauchy problem of a multivalued ordinary differential equation governed by the hypergraph Laplacian, which describes the diffusion of ``heat'' or `…
A Cahn-Hilliard system with forward-backward dynamic boundary condition and non-smooth potentials
Pierluigi Colli, Takeshi Fukao, Luca Scarpa
A system with equation and dynamic boundary condition of Cahn-Hilliard type is considered. This system comes from a derivation performed in Liu-Wu (Arch. Ration. Mech. Anal. 233 (2…
The Cahn-Hilliard equation with forward-backward dynamic boundary condition via vanishing viscosity
Pierluigi Colli, Takeshi Fukao, Luca Scarpa
An asymptotic analysis for a system with equation and dynamic boundary condition of Cahn-Hilliard type is carried out as the coefficient of the surface diffusion acting on the phas…
On a perturbed fast diffusion equation with dynamic boundary conditions
Takeshi Fukao
This paper discusses finite time extinction for a perturbed fast diffusion equation with dynamic boundary conditions. The fast diffusion equation has the characteristic property of…
A second-order accurate structure-preserving scheme for the Cahn-Hilliard equation with a dynamic boundary condition
Makoto Okumura, Takeshi Fukao, Daisuke Furihata +1
We propose a structure-preserving finite difference scheme for the Cahn-Hilliard equation with a dynamic boundary condition using the discrete variational derivative method (DVDM).…
Vanishing diffusion in a dynamic boundary condition for the Cahn-Hilliard equation
Pierluigi Colli, Takeshi Fukao
The initial boundary value problem for a Cahn-Hilliard system subject to a dynamic boundary condition of Allen-Cahn type is treated. The vanishing of the surface diffusion on the d…
Separation property and convergence to equilibrium for the equation and dynamic boundary condition of Cahn-Hilliard type with singular potential
Takeshi Fukao, Hao Wu
We consider a class of Cahn-Hilliard equation that models phase separation process of binary mixtures involving nontrivial boundary interactions in a bounded domain with non-permea…
On a transmission problem for equation and dynamic boundary condition of Cahn-Hilliard type with nonsmooth potentials
Pierluigi Colli, Takeshi Fukao, Hao Wu
This paper is concerned with well-posedness of the Cahn-Hilliard equation subject to a class of new dynamic boundary conditions. The system was recently derived in Liu-Wu (Arch. Ra…
On a coupled bulk-surface Allen-Cahn system with an affine linear transmission condition and its approximation by a Robin boundary condition
Pierluigi Colli, Takeshi Fukao, Kei Fong Lam
We study a coupled bulk-surface Allen-Cahn system with an affine linear transmission condition, that is, the trace values of the bulk variable and the values of the surface variabl…
Cahn-Hilliard equation on the boundary with bulk condition of Allen-Cahn type
Pierluigi Colli, Takeshi Fukao
The well-posedness for a system of partial differential equations and dynamic boundary conditions is discussed. This system is a sort of transmission problem between the dynamics i…
Nonlinear diffusion equations with Robin boundary conditions as asymptotic limits of Cahn-Hilliard systems
Taishi Motoda, Takeshi Fukao
Condition imposed on the nonlinear terms of a nonlinear diffusion equation with {R}obin boundary condition is the main focus of this paper. The degenerate parabolic equations, such…
Nonlinear diffusion equations as asymptotic limits of Cahn--Hilliard systems on unbounded domains via Cauchy's criterion
Takeshi Fukao, Shunsuke Kurima, Tomomi Yokota
This paper develops an abstract theory for subdifferential operators to give existence and uniqueness of solutions to the initial-boundary problem (P) for the nonlinear diffusion e…
Time-dependence of the threshold function in the perfect plasticity model
Takeshi Fukao, Risei Kano
This paper discusses the time-dependence of the threshold function in the perfect plasticity model. In physical terms, it is natural that the threshold function depends on some unk…
Cahn-Hilliard approach to some degenerate parabolic equations with dynamic boundary conditions
Takeshi Fukao
In this paper the well-posedness of some degenerate parabolic equations with a dynamic boundary condition is considered. To characterize the target degenerate parabolic equation fr…
Nonlinear diffusion equations as asymptotic limits of Cahn-Hilliard systems
Pierluigi Colli, Takeshi Fukao
An asymptotic limit of a class of Cahn-Hilliard systems is investigated to obtain a general nonlinear diffusion equation. The target diffusion equation may reproduce a number of we…
Convergence of Cahn-Hilliard systems to the Stefan problem with dynamic boundary conditions
Takeshi Fukao
This paper examines the well-posedness of the Stefan problem with a dynamic boundary condition. To show the existence of the weak solution, the original problem is approximated by…
Equation and dynamic boundary condition of Cahn-Hilliard type with singular potentials
Pierluigi Colli, Takeshi Fukao
The well-posedness of a system of partial differential equations and dynamic boundary conditions, both of Cahn-Hilliard type, is discussed. The existence of a weak solution and its…
Cahn-Hilliard equation with dynamic boundary conditions and mass constraint on the boundary
Pierluigi Colli, Takeshi Fukao
The well-known Cahn-Hilliard equation entails mass conservation if a suitable boundary condition is prescribed. In the case when the equation is also coupled with a dynamic boundar…
The Allen-Cahn equation with dynamic boundary conditions and mass constraints
Pierluigi Colli, Takeshi Fukao
The Allen-Cahn equation, coupled with dynamic boundary conditions, has recently received a good deal of attention. The new issue of this paper is the setting of a rather general ma…