6 citations · 14 across the 5 of their papers we have counts for
5 papers
Optimal control of gradient flows via the Weighted Energy-Dissipation method
Takeshi Fukao, Ulisse Stefanelli, Riccardo Voso
We consider a general optimal control problem in the setting of gradient flows. Two approximations of the problem are presented, both relying on the variational reformulation of gr…
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…
Abstract approach of degenerate parabolic equations with dynamic boundary conditions
Takeshi Fukao, Taishi Motoda
An initial boundary value problem of the nonlinear diffusion equation with a dynamic boundary condition is treated. The existence problem of the initial-boundary value problem is d…
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…
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…