This book covers the main mathematical and numerical models in computational
electrocardiology, ranging from microscopic membrane models of cardiac ionic channels to …

A phase field model for the mixture of two incompressible fluids is presented in this paper.
The model is based on an energetic variational formulation. It consists of a Navier–Stokes …

In this paper, we compute the equilibrium configurations of a vesicle membrane under
elastic bending energy, with prescribed volume and surface area. A variational phase field …

A wildfire model is formulated based on balance equations for energy and fuel, where the
fuel loss due to combustion corresponds to the fuel reaction rate. The resulting coupled …

In this paper we present a new definition for the global in time propagation (motion) of fronts
(hypersurfaces, boundaries) with a prescribed normal velocity, past the first time they …

This is the first of three papers on the Glauber evolution of Ising spin systems with Kac
potentials. We begin with the analysis of the mesoscopic limit, where space scales like the …

We consider an Allen–Cahn type equation of the form ut= Δu+ ε− 2fε (x, t, u), where ε is a
small parameter and fε (x, t, u)= f (u)− εgε (x, t, u) a bistable nonlinearity associated with a …

Abstract We consider the Stefan Problem with surface tension and kinetic undercooling
effects, that is, with the temperature u satisfying the condition u=− σκ− βV on the interface Γ …

In one of the singular limits as interface thickness approaches zero, solutions to the phase
field equations formally approach those of a sharp interface model which incorporates …

We study the full-time dynamics of the initial value problem, for uε= uε (x, t), where 0< ε⪡ 1
and F (u) has global minimum 0 at u=±1. We assume that u0 (·) is bounded, continuous and …