Moving interfaces–and in the stationary case, free boundaries–are ubiquitous in our
environment and daily life. They are at the basis of many physical, chemical, and also …

We use various nonlinear partial differential equations to efficiently solve several surface
modelling problems, including surface blending, N-sided hole filling and free-form surface …

We consider a mass conserving Allen–Cahn equation ut= Δ_ u_+ ε–2 (f (u)–ελ (t)) in a
bounded domain with no flux boundary condition, where ελ (t) is the average of f (u (∙, t)) and …

We study the asymptotic behavior of radially symmetric solutions of the nonlocal equation
ε\phi_t-ε Δ ϕ+ 1 ε W'(ϕ)-\lambda_ ε (t)= 0 in a bounded spherically symmetric domain …

We provide the first general result for the asymptotics of the area preserving mean curvature
flow in two dimensions showing that flat flow solutions, starting from any bounded set of finite …

We present a finite element method for the simulation of all relevant processes of the
evaporation of a liquid droplet suspended in an acoustic levitation device. The mathematical …

We prove:" If M is a compact hypersurface of the hyperbolic space, convex by horospheres
and evolving by the volume preserving mean curvature flow, then it flows for all time …

In this paper, we construct global distributional solutions to the volume-preserving mean-
curvature flow using a variant of the time-discrete gradient flow approach proposed …

We study a moving boundary problem modeling the growth of multicellular spheroids or in
vitro tumors. This model consists of two elliptic equations describing the concentration of a …

We consider the flat flow solution, obtained via a discrete minimizing movement scheme, to
the volume preserving mean curvature flow starting from C 1, 1-regular set. We prove the …