Related papers: Traveling waves for a boundary reaction-diffusion …
The famous Fisher-KPP reaction-diffusion model combines linear diffusion with the typical KPP reaction term, and appears in a number of relevant applications in biology and chemistry. It is remarkable as a mathematical model since it…
In this study, we investigate a porous medium-type flux limited reaction--diffusion equation that arises in morphogenesis modeling. This nonlinear partial differential equation is an extension of the generalized…
We consider an epidemic model with direct transmission given by a system of nonlinear partial differential equations and study the existence of traveling wave solutions. When the basic reproductive number of the considered model is less…
We study capillary-gravity surface waves for fluid flows governed by Darcy's law. This includes flows in vertical Hele-Shaw cells and in porous media (the one-phase Muskat problem) with finite or infinite depth. The free boundary is acted…
The wave-like nature of electrons leads to the existence of upper bounds on the thermoelectric response of nanostructured devices [R. S. Whitney, Phys. Rev. Lett. 112, 130601 (2014); Phys. Rev. B 91, 115425 (2015)]. This fundamental result,…
Starting from the kinetic approach for a mixture of reacting gases whose particles interact through elastic scattering and a bimolecular reversible chemical reaction, the equations that govern the dynamics of the system are obtained by…
Regimes of chemical reaction wave propagating in reactive gaseous mixtures, whose chemistry is governed by chain-branching kinetics, are studied depending on the characteristics of a transient thermal energy deposition localized in a finite…
Stability of a set of travelling wave solutions to the hyperbolic generalization of the convection-reaction-diffusion equation is studied by means of the qualitative methods and numerical simulation.
New travelling wave solutions to the Fornberg-Whitham equation are investigated. They are characterized by two parameters. The expresssions for the periodic and solitary wave solutions are obtained.
We study the existence and uniqueness of a solution to a linear stationary convection-diffusion equation stated in an infinite cylinder, Neumann boundary condition being imposed on the boundary. We assume that the cylinder is a junction of…
Many reaction-diffusion models produce travelling wave solutions that can be interpreted as waves of invasion in biological scenarios such as wound healing or tumour growth. These partial differential equation models have since been adapted…
In this paper, we consider the stabilization of wave equations with moving boundary. First, we show the solution behaviour of wave equation with Neumann boundary conditions, that is, the energy of wave equation with mixed boundary…
We extend earlier work on traveling waves in premixed flames in a gravitationally stratified medium, subject to the Boussinesq approximation. For three-dimensional channels not aligned with the gravity direction and under the Dirichlet…
The use of fully or partially absorbing boundary conditions for diffusion-based problems has become paradigmatic in physical chemistry and biochemistry to describe reactions occurring in solutions or in living media. However, as chemical…
We study the heat equation in the exterior of the unit ball with a linear dynamical boundary condition. Our main aim is to find upper and lower bounds for the rate of convergence to solutions of the Laplace equation with the same dynamical…
Many monostable reaction-diffusion equations admit one-dimensional travelling waves if and only if the wave speed is sufficiently high. The values of these minimum wave speeds are not known exactly, except in a few simple cases. We present…
This paper is concerned with the blow-up property of solutions to an initial boundary value problem for a reaction diffusion equation with special diffusion processes. It is shown, under certain conditions on the initial data, that the…
The existence of global weak solutions to a parabolic energy-transport system in a bounded domain with no-flux boundary conditions is proved. The model can be derived in the diffusion limit from a kinetic equation with a linear collision…
We study linear stability of planar travelling waves for a scalar reaction-diffusion equation with non-linear anisotropic diffusion. The mathematical model is derived from the full thermo-hydrodynamical model describing the process of…
We consider the quartic focusing Half Wave equation (HW) in one space dimension. We show first that that there exist traveling wave solutions with arbitrary small $H^{\frac 12}(\R)$ norm. This fact shows that small data scattering is not…