6 papers · 1 filter
Stability of stationary reaction diffusion-degenerate Nagumo fronts I: spectral analysis
Raffaele Folino, César A. Hernández Melo, Luis F. López RÃos +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…
Layer dynamics for the Allen-Cahn equation with nonlinear phase-dependent diffusion
José Alejandro Butanda MejÃa, 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_…
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…
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…
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…