Physical review. E, Statistical, nonlinear, andâ€¦

2014

The topology and the geometry of a surface play a fundamental role in determining the equilibrium configurations of thin films of liquid crystals. We propose here a theoretical analysis of a recentlyâ€¦ (More)

This paper addresses the long-time behaviour of gradient flows of non convex functionals in Hilbert spaces. Exploiting the notion of generalized semiflows by J. M. Ball, we provide some sufficientâ€¦ (More)

We study a Penrose-Fife phase transition model coupled with homogeneous Neumann boundary conditions. Improving previous results, we show that the initial value problem for this model admits a uniqueâ€¦ (More)

A doubly nonlinear parabolic equation of the form Î±(u t) âˆ’ âˆ†u + W â€² (u) = f , complemented with initial and either Dirichlet or Neumann homogeneous boundary conditions, is addressed. The twoâ€¦ (More)

We consider a hydrodynamic system that models the Smectic-A liquid crystal flow. The model consists of the Navier-Stokes equation for the fluid velocity coupled with a fourth-order equation for theâ€¦ (More)

We develop the long-time analysis for gradient flow equations in metric spaces. In particular, we consider two notions of solutions for metric gradient flows, namely energy and generalized solutions.â€¦ (More)

We show non-existence of solutions of the Cauchy problem in R for the nonlinear parabolic equation involving fractional diffusion âˆ‚tu + (-âˆ†) s Ï†(u) = 0, with 0 < s < 1 and very singularâ€¦ (More)

We establish new quantitative estimates for localized finite differences of solutions to the Poisson problem for the fractional Laplace operator with homogeneous Dirichlet conditions of solid typeâ€¦ (More)

Modelling a crystal with impurities we study an atomic chain of point masses with linear nearest neighbour interactions. We assume that the masses of the particles are normalised to 1, except for oneâ€¦ (More)