87 citations · 466 across the 33 of their papers we have counts for
23 papers · 1 filter
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…
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…
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…
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…
A multiphase Cahn-Hilliard-Darcy model for tumour growth with necrosis
Harald Garcke, Kei Fong Lam, Robert Nürnberg +1
We derive a Cahn-Hilliard-Darcy model to describe multiphase tumour growth taking interactions with multiple chemical species into account as well as the simultaneous occurrence of…
On a Cahn--Hilliard--Darcy system for tumour growth with solution dependent source terms
Harald Garcke, Kei Fong Lam
We study the existence of weak solutions to a mixture model for tumour growth that consists of a Cahn--Hilliard--Darcy system coupled with an elliptic reaction-diffusion equation.…
Global weak solutions and asymptotic limits of a Cahn--Hilliard--Darcy system modelling tumour growth
Harald Garcke, Kei Fong Lam
We study the existence of weak solutions to a Cahn--Hilliard--Darcy system coupled with a convection-reaction-diffusion equation through the fluxes, through the source terms and in…
Analysis of a Cahn--Hilliard system with non-zero Dirichlet conditions modeling tumor growth with chemotaxis
Harald Garcke, Kei Fong Lam
We consider a diffuse interface model for tumor growth consisting of a Cahn--Hilliard equation with source terms coupled to a reaction-diffusion equation, which models a tumor grow…
Well-posedness of a Cahn--Hilliard system modelling tumour growth with chemotaxis and active transport
Harald Garcke, Kei Fong Lam
We consider a diffuse interface model for tumour growth consisting of a Cahn--Hilliard equation with source terms coupled to a reaction-diffusion equation. The coupled system of pa…
A Cahn--Hilliard--Darcy model for tumour growth with chemotaxis and active transport
Harald Garcke, Kei Fong Lam, Emanuel Sitka +1
Using basic thermodynamic principles we derive a Cahn--Hilliard--Darcy model for tumour growth including nutrient diffusion, chemotaxis, active transport, adhesion, apoptosis and p…
Analysis of the diffuse domain approach for a bulk-surface coupled PDE system
Helmut Abels, Kei Fong Lam, Björn Stinner
We analyse a diffuse interface type approximation, known as the diffuse domain approach, of a linear coupled bulk-surface elliptic partial differential system. The well-posedness o…