Biological Aggregation Driven by Social and Environmental Factors: A Nonlocal Model and Its Degenerate Cahn-Hilliard Approximation

Volume preserving mean curvature flow as a limit of a nonlocal Ginzburg-Landau equation

We study the asymptotic behaviour of radially symmetric solutions of the nonlocal equation In a bounded spherically symmetric domain ft C R"f where A,(<) m 1 fftW(<p) «fcr, with a Neumann boundary condition. The analysis is based on "energy methods combined with some a-priori estimates, the latter being used to approximate the sohtion by the first two terms of an asymptotic expansionWe only nee...

Coarsening in Nonlocal Interfacial Systems

We consider coarsening in interfacial systems driven by nonlocal energies. Of particular interest are the nonlocal Cahn–Hilliard equation and models of biological aggregation. The energies considered cause the system to separate into phases. The pattern of interfaces evolves under nonlocal surfacetension-type effects. The typical length scales grow and the pattern coarsens. We prove a rigorous ...

On the Cahn{hilliard Equation with Non{constant Mobility and Its Asymptotic Limit

We present an existence result for the Cahn{Hilliard equation with a concentration dependent mobility which allows the mobility to degenerate. Formal asymptotic results relate the Cahn{Hilliard equation with a degenerate mobility to motion by surface diiusion V = ? S. We state a local existence result for this geometric motion and show that circles are asymptotically stable.

Finite Element Approximation of a Degenerate Allen-Cahn/Cahn-Hilliard System

On a diffuse interface model for tumour growth with non-local interactions and degenerate mobilities

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 system consists of a Cahn–Hilliard equation coupled to a reactiondiffusion equation. For non-degenerate mobilities and smooth potentials, we derive well-posedness results, which are the non-local analogue of those obt...