Related papers: A fractional framework for perimeters and phase tr…
We prove that certain nonlocal functionals defined on partitions made of measurable sets Gamma-converge to a local functional modeled on the perimeter in the sense of De Giorgi. Those nonlocal functionals involve generalized surface tension…
This is a review of statistical inference methodology for stochastic differential equations driven by fractional Brownian motion, otherwise called fractional diffusions. The first section reviews the theory needed to rigorously define them.…
The multi-phase-field approach is generalized to treat capillarity-driven diffusion parallel to the surfaces and phase-boundaries, i.e. the boundaries between a condensed phase and its vapor and the boundaries between two or multiple…
Spectral analysis has long been recognized as a fundamental tool for studying the existence, uniqueness, and qualitative behavior of solutions to semilinear elliptic and parabolic equations, as well as their long-time dynamics. In modern…
This doctoral thesis is devoted to the analysis of some minimization problems that involve nonlocal functionals. We are mainly concerned with the $s$-fractional perimeter and its minimizers, the $s$-minimal sets. We investigate the behavior…
In this paper we examine boundary effects in a fractional chemotactic equation derived from a kinetic transport model describing cell movement in response to chemical gradients (chemotaxis). Specifically, we analyze reflecting boundary…
Many physical phenomena occur on domains that grow in time. When the timescales of the phenomena and domain growth are comparable, models must include the dynamics of the domain. A widespread intrinsically slow transport process is…
The recently proposed universal relations between the moments of the polydispersity distributions of a phase-separated weakly polydisperse system are analyzed in detail using the numerical results obtained by solving a simple density…
We consider the nonlinear degenerate parabolic equation of porous medium type, whose diffusion is driven by the (spectral) fractional Laplacian on the hyperbolic space. We provide existence results for solutions, in an appropriate weak…
We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem in perforated domains.
In this technical report we analyse the performance of diffusion strategies applied to the Least-Mean-Square adaptive filter. We configure a network of cooperative agents running adaptive filters and discuss their behaviour when compared…
In this article we derive the fractional porous medium equation for any power of the fractional Laplacian as the hydrodynamic limit of a microscopic dynamics of random particles with long range interactions, but the jump rate highly depends…
In this paper we state some sharp maximum principle, i.e. we characterize the geometry of the sets of minima for supersolutions of equations involving the $k$-\emph{th fractional truncated Laplacian} or the $k$-\emph{th fractional…
This paper studies the intermediate time behaviour of a small random perturbation of a periodic cellular flow. Our main result shows that on time scales shorter than the diffusive time scale, the limiting behaviour of trajectories that…
We study reaction-diffusion equations in cylinders with possibly nonlinear diffusion and possibly nonlinear Neumann boundary conditions. We provide a geometric Poincar\'e-type inequality and classification results for stable solutions, and…
We introduce a minimization formulation for the determination of a finite-dimensional, time-dependent, orthonormal basis that captures directions of the phase space associated with transient instabilities. While these instabilities have…
A non-isothermal phase field model that captures both displacive and diffusive phase transformations in a unified framework is presented. The model is developed in a formal thermodynamic setting, which provides guidance on admissible…
We consider a fractional Plateau's problem dealing with sets with prescribed non-local mean curvature. This problem can be seen as a non-local counterpart of the classical Massari's Problem. We obtain existence and regularity results,…
We study in this note the Fisher-KPP equation where the Laplacian is replaced by the generator of a Feller semigroup with slowly decaying kernel, an important example being the fractional Laplacian. Contrary to what happens in the standard…
A dynamical system framework is used to describe transport processes in plasmas embedded in a magnetic field. For periodic systems with one degree of freedom the Poincar\'e map provides a splitting of the phase space into regions where…