Related papers: Steady-State Solutions in Nonlinear Diffusive Shoc…
We propose fractional Fokker-Planck equation for the kinetic description of relaxation and superdiffusion processes in constant magnetic and random electric fields. We assume that the random electric field acting on a test charged particle…
Possible formulations of the problem of cosmic rays acceleration in the interstellar galactic medium are considered with the use of fractional differential equations. The applied technique has been physically justified. A Fermi result has…
This paper establishes the spectral stability in exponentially weighted spaces of smooth traveling monotone fronts for reaction diffusion equations of Fisher-KPP type with nonlinear degenerate diffusion coefficient. It is assumed that the…
We describe acceleration of the front propagation for solutions to a class of monostable nonlinear equations with a nonlocal diffusion in $\mathbb{R}^d$, $d\geq1$. We show that the acceleration takes place if either the diffusion kernel or…
We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the…
We consider spatially discrete bistable reaction-diffusion equations that admit wave front solutions. Depending on the parameters involved, such wave fronts appear to be pinned or to glide at a certain speed. We study the transition of…
The dynamics of a one-degree of freedom oscillator with arbitrary polynomial non-linearity subjected to an external periodic excitation is studied. The sequences (cascades) of harmonic and subharmonic stationary solutions to the equation of…
A system of partial differential equations representing stochastic neural fields was recently proposed with the aim of modelling the activity of noisy grid cells when a mammal travels through physical space. The system was rigorously…
We show that propagation speeds in invasion processes modeled by reaction-diffusion systems are determined by marginal spectral stability conditions, as predicted by the marginal stability conjecture. This conjecture was recently settled in…
Considering the example of interacting Brownian particles we present a linear response derivation of the boundary condition for the corresponding hydrodynamic description (the diffusion equation). This requires us to identify a non-analytic…
We provide a `user guide' to the literature of the past twenty years concerning the modeling and approximation of discontinuous solutions to nonlinear hyperbolic systems that admit small-scale dependent shock waves. We cover several classes…
We study the escape rate of a particle in a metastable potential in presence of a dissipative bath coupled to the momentum of the particle. Using the semiclassical bounce technique, we find that this rate is exponentially enhanced. In…
We show here that a purely kinetic approach to the excitation of waves by cosmic rays in the vicinity of a shock front leads to predict the appearance of a non-alfvenic fastly growing mode which is the same that was found by Bell (2004) by…
We devote this paper to the issue of existence of pulsating travelling front solutions for spatially periodic heterogeneous reaction-diffusion equations in arbitrary dimension, in both bistable and more general multistable frameworks. In…
The current paper is concerned with positive stationary solutions and spatial spreading speeds of KPP type evolution equations with random or nonlocal or discrete dispersal in locally spatially inhomogeneous media. It is shown that such an…
The physics of activated escape of objects out of a metastable state plays a key role in diverse scientific areas involving chemical kinetics, diffusion and dislocation motion in solids, nucleation, electrical transport, motion of flux…
We develop an unconditionally energy-stable tensor-product space-time discretization framework for the solution of a linear kinetic transport equation in one space dimension. The kinetic equation is a simplified model of radiative transfer…
Recent gamma ray observations show that middle aged supernova remnants interacting with molecular clouds can be sources of both GeV and TeV emission. Models involving re-acceleration of pre-existing cosmic rays in the ambient medium and…
The observed energy spectra of accelerated particles at interplanetary shocks often do not match the diffusive shock acceleration (DSA) theory predictions. In some cases, the particle flux forms a plateau over a wide range of energies,…
Reaction-diffusion equations appear in biology and chemistry, and combine linear diffusion with different kind of reaction terms. Some of them are remarkable from the mathematical point of view, since they admit families of travelling waves…