38 citations · 168 across the 29 of their papers we have counts for
35 papers
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…
Orbital instability of periodic waves for generalized Korteweg-de Vries-Burgers equations with a source
Anna Naumkina, Ramón G. Plaza
A family of generalized Korteweg-de Vries-Burgers equations in one space dimension with a nonlinear source is considered. The purpose of this contribution is twofold. On one hand,…
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…
Well-posedness and decay structure of a quantum hydrodynamics system with Bohm potential and linear viscosity
Ramón G. Plaza, Delyan Zhelyazov
In this paper, a compressible viscous-dispersive Euler system in one space dimension in the context of quantum hydrodynamics is considered. The purpose of this study is twofold. Fi…
Global decay of perturbations of equilibrium states for one-dimensional heat conducting compressible fluids of Korteweg type
Ramón G. Plaza, José M. Valdovinos
This paper studies the one dimensional Navier-Stokes-Fourier-Korteweg system of equations describing the evolution of a heat-conducting compressible fluid that exhibits viscosity a…
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…
Orbital instability of periodic waves for scalar viscous balance laws
Enrique Álvarez, Jaime Angulo Pava, Ramón G. Plaza
The purpose of this paper is to prove that, for a large class of nonlinear evolution equations known as scalar viscous balance laws, the spectral (linear) instability condition of…
Analysis and numerics of the propagation speed for hyperbolic reaction-diffusion models
Corrado Lattanzio, Corrado Mascia, Ramon G. Plaza +1
In this paper, we analyse propagating fronts in the context of hyperbolic theories of dissipative processes. These can be considered as a natural alternative to the more classical…
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…
Dissipative structure of one-dimensional isothermal compressible fluids of Korteweg type
Ramón G. Plaza, José Manuel Valdovinos
This paper studies the dissipative structure of the system of equations that describes the motion of a compressible, isothermal, viscous-capillar fluid of Korteweg type in one spac…
Spectral instability of small-amplitude periodic waves for hyperbolic non-Fickian diffusion advection models with logistic source
Enrique Álvarez, Ricardo Murillo, Ramón G. Plaza
A hyperbolic model for diffusion, nonlinear transport (or advection) and production of a scalar quantity, is considered. The model is based on a constitutive law of Cattaneo-Maxwel…
Instability theory of kink and anti-kink profiles for the sine-Gordon equation on Josephson tricrystal boundaries
Jaime Angulo Pava, Ramón G. Plaza
The aim of this work is to establish a instability study for stationary kink and antikink/kink profiles solutions for the sine-Gordon equation on a metric graph with a structure re…
Unstable kink and anti-kink profile for the sine-Gordon equation on a -junction graph with -interaction at the vertex
Jaime Angulo Pava, Ramón G. Plaza
The sine-Gordon equation on a metric graph with a structure represented by a -junction, is considered. The model is endowed with boundary conditions at the graph-verte…
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…
Stability of classical shock fronts for compressible hyperelastic materials of Hadamard type
Ramón G. Plaza, Fabio Vallejo
This paper studies the uniform and weak Lopatinski\uı conditions associated to classical (Lax) shock fronts of arbitrary amplitude for compressible hyperelastic materials of Hadama…
Existence and spectral instability of bounded spatially periodic traveling waves for scalar viscous balance laws
Enrique Alvarez, Ramon G. Plaza
This paper studies both existence and spectral stability properties of bounded spatially periodic traveling wave solutions to a large class of scalar viscous balance laws in one sp…
Unstable kink-soliton profiles for the sine-Gordon equation on a -junction graph with -interaction
Jaime Angulo Pava, Ramón G. Plaza
The aim of this work is to establish a linear instability result of stationary, kink and kink/anti-kink soliton profile solutions for the sine-Gordon equation on a metric graph wit…
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'…
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…
Spectral stability of monotone traveling fronts for reaction diffusion-degenerate Nagumo equations
J. Francisco Leyva, Luis F. López Ríos, Ramón G. Plaza
This paper establishes the spectral stability of monotone traveling front solutions for reaction-diffusion equations where the reaction function is of Nagumo (or bistable) type and…
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…
Orbital stability of standing waves for the nonlinear Schrödinger equation with attractive delta potential and double power repulsive nonlinearity
Jaime Angulo Pava, César A. Hernández Melo, Ramón G. Plaza
In this paper, a nonlinear Schrödinger equation with an attractive (focusing) delta potential and a repulsive (defocusing) double power nonlinearity in one spatial dimension is con…
On the role of cancer cells' diffusion in the tumor growth paradox
Isai Padilla, Ramón G. Plaza
In this contribution, the non-local, integro-partial differential system of equations proposed by Hillen et al. (Bull. Math. Biol. 75, 2013, no.1, 161-184) to account for the the t…
Strict dissipativity of Cattaneo-Christov systems for compressible fluid flow
Felipe Angeles, Carlos Malaga, Ramon G. Plaza
This work considers a compressible, viscous, heat-conducting fluid exhibiting thermal relaxation according to Christov's constitutive heat transfer law (C. I. Christov, Mech. Resea…