11 citations · 98 across the 23 of their papers we have counts for
24 papers
Slow motion for the time-fractional Allen-Cahn equation with linear and nonlinear diffusion
Davide Cusseddu, Raffaele Folino, Luis Fernando López Ríos
We study the slow motion of phase transition layers for a time-fractional Allen--Cahn equation with a Caputo time derivative of order . We show that the fractional memor…
Stability of stationary reaction diffusion-degenerate Nagumo fronts I: spectral analysis
Raffaele Folino, César A. Hernández Melo, Luis F. López Ríos +1
This paper establishes the spectral stability of monotone, stationary front solutions for reaction-diffusion equations where the reaction function is of Nagumo (or bistable) type a…
Existence and spectral stability analysis of viscous-dispersive shock profiles for isentropic compressible fluids of Korteweg type
R. Folino, C. Lattanzio, R. G. Plaza
The system describing the dynamics of a compressible isentropic fluid exhibiting viscosity and internal capillarity in one space dimension and in Lagrangian coordinates, is conside…
Stability properties of solutions to convection-reaction equations with nonlinear diffusion
Alessandro Alla, Alessandra De Luca, Raffaele Folino +1
In this paper we study a convection-reaction-diffusion equation of the form \begin{equation*} u_t=\varepsilon(h(u)u_x)_x-f(u)_x+f'(u), \quad t>0, \end{equation*} with a nonlinear d…
Layer dynamics for the Allen-Cahn equation with nonlinear phase-dependent diffusion
José Alejandro Butanda Mejía, Daniel Castañon Quiroz, Raffaele Folino +1
The goal of this paper is to describe the metastable dynamics of the solutions to the reaction-diffusion equation with nonlinear phase-dependent diffusion $u_t=\varepsilon^2(D(u)u_…
Instability of periodic waves for the Korteweg-de Vries-Burgers equation with monostable source
Raffaele Folino, Anna Naumkina, Ramón G. Plaza
In this paper, it is proved that the KdV-Burgers equation with a monostable source term of Fisher-KPP type has small-amplitude periodic traveling wave solutions with finite fundame…
Layered patterns in reaction-diffusion models with Perona-Malik diffusions
Alessandra De Luca, Raffaele Folino, Marta Strani
In this paper we deal with a reaction-diffusion equation in a bounded interval of the real line with a nonlinear diffusion of Perona-Malik's type and a balanced bistable reaction t…
Minimization of a Ginzburg-Landau functional with mean curvature operator in 1-D
Raffaele Folino, Corrado Lattanzio
The aim of this paper is to investigate the minimization problem related to a Ginzburg-Landau energy functional, where in particular a nonlinear diffusion of mean curvature-type is…
Spectral stability of weak dispersive shock profiles for quantum hydrodynamics with nonlinear viscosity
Raffaele Folino, Ramón G. Plaza, Delyan Zhelyazov
This paper studies the stability of weak dispersive shock profiles for a quantum hydrodynamics system in one space dimension with nonlinear viscosity and dispersive (quantum) effec…
Spectral stability of small-amplitude dispersive shocks in quantum hydrodynamics with viscosity
Raffaele Folino, Ramón G. Plaza, Delyan Zhelyazov
A compressible viscous-dispersive Euler system in one space dimension in the context of quantum hydrodynamics is considered. The dispersive term is due to quantum effects described…
On a generalized Cahn-Hilliard model with p-Laplacian
Raffaele Folino, Luis Fernando Lopez Rios, Marta Strani
A generalized Cahn-Hilliard model in a bounded interval of the real line with no-flux boundary conditions is considered. The label "generalized" refers to the fact that we consider…
Long-time behavior of solutions to the generalized Allen-Cahn model with degenerate diffusivity
Raffaele Folino, Luis F. López Ríos, Ramón G. Plaza
The generalized Allen-Cahn equation, \[ u_t=\varepsilon^2(D(u)u_x)_x-\frac{\varepsilon^2}2D'(u)u_x^2-F'(u), \] with nonlinear diffusion, , and potential, , of t…
Long time dynamics of solutions to -Laplacian diffusion problems with bistable reaction terms
Raffaele Folino, Ramón G. Plaza, Marta Strani
This paper establishes the emergence of slowly moving transition layer solutions for the -Laplacian (nonlinear) evolution equation, \[ u_t = \varepsilon^p(|u_x|^{p-2}u_x)_x - F'…
Metastable dynamics for a hyperbolic variant of the mass conserving Allen-Cahn equation in one space dimension
Raffaele Folino
In this paper, we consider some hyperbolic variants of the mass conserving Allen-Cahn equation, which is a nonlocal reaction-diffusion equation, introduced (as a simpler alternativ…
Exponentially slow motion of interface layers for the one-dimensional Allen-Cahn equation with nonlinear phase-dependent diffusivity
Raffaele Folino, César Hernández Melo, Luis López Ríos +1
This paper considers a one-dimensional generalized Allen-Cahn equation of the form \[ u_t = \varepsilon^2 (D(u)u_x)_x - f(u), \] where is constant, is a po…
Metastable patterns for a reaction-diffusion model with mean curvature-type diffusion
Raffaele Folino, Ramón G. Plaza, Marta Strani
Reaction-diffusion equations are widely used to describe a variety of phenomena such as pattern formation and front propagation in biological, chemical and physical systems. In the…
On the speed rate of convergence of solutions to conservation laws with nonlinear diffusions
Raffaele Folino, Marta Strani
In this paper we analyze the long-time behavior of solutions to conservation laws with nonlinear diffusion terms of different types: saturating dissipation (monotone and non monoto…
Metastability and layer dynamics for the hyperbolic relaxation of the Cahn-Hilliard equation
Raffaele Folino, Corrado Lattanzio, Corrado Mascia
The goal of this paper is to accurately describe the metastable dynamics of the solutions to the hyperbolic relaxation of the Cahn-Hilliard equation in a bounded interval of the re…
Stability properties and dynamics of solutions to viscous conservation laws with mean curvature operator
Raffaele Folino, Maurizio Garrione, Marta Strani
In this paper we study the long time dynamics of the solutions to the initial-boundary value problem for a scalar conservation law with a saturating nonlinear diffusion. After disc…
Motion of interfaces for a damped hyperbolic Allen-Cahn equation
Raffaele Folino, Corrado Lattanzio, Corrado Mascia
Consider the Allen-Cahn equation , where is a double well potential with wells of equal depth, located at . There are a lot of papers devoted t…
Slow dynamics for the hyperbolic Cahn-Hilliard equation in one space dimension
Raffaele Folino, Corrado Lattanzio, Corrado Mascia
The aim of this paper is to study the metastable properties of the solutions to a hyperbolic relaxation of the classic Cahn-Hilliard equation in one space dimension, subject to eit…
Slow motion for one-dimensional nonlinear damped hyperbolic Allen-Cahn systems
Raffaele Folino
We consider a nonlinear damped hyperbolic reaction-diffusion system in a bounded interval of the real line with homogeneous Neumann boundary conditions and we study the metastable…
Metastable dynamics for hyperbolic variations of the Allen-Cahn equation
Raffaele Folino, Corrado Lattanzio, Corrado Mascia
Metastable dynamics of a hyperbolic variation of the Allen-Cahn equation with homogeneous Neumann boundary conditions are considered. Using the "dynamical approach" proposed by Car…
Slow motion for a hyperbolic variation of Allen-Cahn equation in one space dimension
Raffaele Folino
The aim of this paper is to prove that, for specific initial data and with homogeneous Neumann boundary conditions, the solution of the IBVP for a hyperbolic variation…