87 citations · 466 across the 33 of their papers we have counts for
39 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…
On a Mullins-Sekerka model for the growth of active droplets modelling protocells: Stability analysis and numerical computations
Harald Garcke, Kei Fong Lam, Robert Nürnberg +1
Mullins-Sekerka models with chemical reactions can lead to scenarios where droplets grow, become unstable, split, grow and undergo further division. These grow and division cycles…
On a Cahn-Hilliard equation for the growth and division of chemically active droplets modeling protocells
Harald Garcke, Kei Fong Lam, Robert Nürnberg +1
The Cahn-Hilliard model with reaction terms can lead to situations in which no coarsening is taking place and, in contrast, growth and division of droplets occur which all do not g…
Stability and convergence of relaxed scalar auxiliary variable schemes for Cahn-Hilliard systems with bounded mass source
Kei Fong Lam, Ru Wang
The scalar auxiliary variable (SAV) approach of Shen et al. (2018), which presents a novel way to discretize a large class of gradient flows, has been extended and improved by many…
Numerical analysis of a FE/SAV scheme for a Caginalp phase field model with mechanical effects in stereolithography
Xingguang Jin, Kei Fong Lam, Changqing Ye
In this work we propose a phase field model based on a Caginalp system with mechanical effects to study the underlying physical and chemical processes behind stereolithography, whi…
Phase field topology optimisation for 4D printing
Harald Garcke, Kei Fong Lam, Robert Nürnberg +1
This work concerns a structural topology optimisation problem for 4D printing based on the phase field approach. The concept of 4D printing as a targeted evolution of 3D printed st…
Overhang penalization in additive manufacturing via phase field structural topology optimization with anisotropic energies
Harald Garcke, Kei Fong Lam, Robert Nürnberg +1
A phase field approach for structural topology optimization with application to additive manufacturing is analyzed. The main novelty is the penalization of overhangs (regions of th…
Sparse optimal control of a phase field tumour model with mechanical effects
Harald Garcke, Kei Fong Lam, Andrea Signori
In this paper, we study an optimal control problem for a macroscopic mechanical tumour model based on the phase field approach. The model couples a Cahn--Hilliard type equation to…
On the Existence of Strong Solutions to the Cahn-Hilliard-Darcy system with mass source
Andrea Giorgini, Kei Fong Lam, Elisabetta Rocca +1
We study a diffuse interface model describing the evolution of the flow of a binary fluid in a Hele-Shaw cell. The model consists of a Cahn-Hilliard-Darcy (CHD) type system with tr…
Strong well-posedness and inverse identification problem of a non-local phase field tumor model with degenerate mobilities
S. Frigeri, K. F. Lam, A. Signori
We extend previous weak well-posedness results obtained in Frigeri et al. (2017) concerning a non-local variant of a diffuse interface tumor model proposed by Hawkins-Daarud et al.…
Phase-field dynamics with transfer of materials: The Cahn--Hilliard equation with reaction rate dependent dynamic boundary conditions
Patrik Knopf, Kei Fong Lam, Chun Liu +1
The Cahn--Hilliard equation is one of the most common models to describe phase separation processes of a mixture of two materials. For a better description of short-range interacti…
On a phase field model of Cahn-Hilliard type for tumour growth with mechanical effects
Harald Garcke, Kei Fong Lam, Andrea Signori
Mechanical effects have mostly been neglected so far in phase field tumour models that are based on a Cahn-Hilliard approach. In this paper we study a macroscopic mechanical model…
Weak and stationary solutions to a Cahn-Hilliard-Brinkman model with singular potentials and source terms
Matthias Ebenbeck, Kei Fong Lam
We study a phase field model proposed recently in the context of tumour growth. The model couples a Cahn-Hilliard-Brinkman (CHB) system with a elliptic reaction-diffusion equation…
Convergence of a Robin boundary approximation for a Cahn--Hilliard system with dynamic boundary conditions
Patrik Knopf, Kei Fong Lam
We prove the existence of unique weak solutions to an extension of a Cahn--Hilliard model proposed recently by C.~Liu and H.~Wu (2019), in which the new dynamic boundary condition…
Sharp interface limit of a non-mass-conserving Cahn--Hilliard system with source terms and non-solenoidal Darcy flow
Kei Fong Lam
We study the sharp interface limit of a non-mass-conserving Cahn--Hilliard--Darcy system with the weak compactness method developed in Chen (J. Differential Geometry, 1996). The so…
Convergence to equilibrium for a bulk--surface Allen--Cahn system coupled through a Robin boundary condition
Kei Fong Lam, Hao Wu
We consider a coupled bulk--surface Allen--Cahn system affixed with a Robin-type boundary condition between the bulk and surface variables. This system can also be viewed as a rela…
Phase field modelling of surfactants in multi-phase flow
Oliver R. A. Dunbar, Kei Fong Lam, Bjorn Stinner
A diffuse interface model for surfactants in multi-phase flow with three or more fluids is derived. A system of Cahn-Hilliard equations is coupled with a Navier-Stokes system and a…
Bayesian parameter identification in Cahn-Hilliard models for biological growth
Christian Kahle, Kei Fong Lam, Jonas Latz +1
We consider the inverse problem of parameter estimation in a diffuse interface model for tumour growth. The model consists of a fourth-order Cahn-Hilliard system and contains three…
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 inpainting with the double obstacle potential
Harald Garcke, Kei Fong Lam, Vanessa Styles
The inpainting of damaged images has a wide range of applications, and many different mathematical methods have been proposed to solve this problem. Inpainting with the help of Cah…
On a multi-species Cahn-Hilliard-Darcy tumor growth model with singular potentials
Sergio Frigeri, Kei Fong Lam, Elisabetta Rocca +1
We consider a model describing the evolution of a tumor inside a host tissue in terms of the parameters , (proliferating and dead cells, respectively), (cell velocit…
Parameter identification via optimal control for a Cahn--Hilliard-chemotaxis system with a variable mobility
Christian Kahle, Kei Fong Lam
We consider the inverse problem of identifying parameters in a variant of the diffuse interface model for tumour growth model proposed by Garcke, Lam, Sitka and Styles (Math. Model…
On a diffuse interface model for tumour growth with non-local interactions and degenerate mobilities
Sergio Frigeri, Kei Fong Lam, Elisabetta Rocca
We study a non-local variant of a diffuse interface model proposed by Hawkins--Darrud et al. (2012) for tumour growth in the presence of a chemical species acting as nutrient. The…
Thermodynamically Consistent Navier--Stokes--Cahn--Hilliard Models with Mass Transfer and Chemotaxis
Kei Fong Lam, Hao Wu
We derive a class of Navier--Stokes--Cahn--Hilliard systems that models two-phase flows with mass transfer coupled to the process of chemotaxis. These thermodynamically consistent…