Related papers: Traveling fronts in a reaction-diffusion equation …
Analysis of the speed of propagation in parabolic operators is frequently carried out considering the minimal speed at which its traveling waves move. This value depends on the solution concept being considered. We analyze an extensive…
In the mean-field theory of magnetic fields, turbulent transport, i.e. the turbulent electromotive force, is described by a combination of the alpha effect and turbulent magnetic diffusion, which are usually assumed to be proportional…
The current paper is devoted to the study of existence and non-existence of transition fronts for two species competition lattice system in random media, and explore the influence of randomness of the media on the wave profiles and wave…
We consider a one-dimensional reaction-diffusion equation of Fisher-Kolmogoroff-Petrovsky-Piscounoff type. We investigate the effect of the interaction between the nonlinear diffusion coefficient and the reaction term on the existence and…
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…
The spatial and temporal persistence, or first-return distributions are measured for slow combustion fronts in paper. The stationary temporal and (perhaps less convincingly) spatial persistence exponents agree with the predictions based on…
We are concerned with large scale magnetic field dynamo generation and propagation of magnetic fronts in turbulent electrically conducting fluids. An effective equation for the large scale magnetic field is developed here that takes into…
This paper is concerned with curved fronts of bistable reaction-diffusion equations in spatially periodic media for dimensions $N\geq 2$. The curved fronts concerned are transition fronts connecting $0$ and $1$. Under a priori assumption…
The propagation of fronts in the Fisher-Kolmogorov equation with spatially varying diffusion coefficients is studied. Using coordinate changes, WKB approximations, and multiple scales analysis, we provide an analytic framework that…
Using pointwise semigroup techniques, we establish sharp rates of decay in space and time of a perturbed reaction diffusion front to its time-asymptotic limit. This recovers results of Sattinger, Henry and others of time-exponential…
Motivated by earlier studies of artificial perceptions of light called phosphenes, we analyze traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators modeling this phenomenon. We examine the discrete model…
We consider the propagation of a flame front in a solid medium with a periodic structure. The model is governed by a free boundary system for the pair" temperature-front. "The front's normal velocity depends on the temperature via a…
We deal with heteroclinic planar fronts for parameter-dependent reaction-diffusion equations with bistable reaction and saturating diffusive term like $$ u_t=\epsilon \, \textrm{div}\, \left(\frac{\nabla u}{\sqrt{1+\vert \nabla u…
We study a one-dimensional reaction-diffusion system which describes an isothermal autocatalytic chemical reaction involving both a quadratic (A + B -> 2B) and a cubic (A + 2B -> 3B) autocatalysis. The parameters of this system are the…
We study a system of interacting particles in a periodically moving external potential, within the simplest possible description of paradigmatic symmetric exclusion process on a ring. The model describes diffusion of hardcore particles…
This paper is concerned with the analysis of speed-up of reaction-diffusion-advection traveling fronts in infinite cylinders with periodic boundary conditions. The advection is a shear flow with a large amplitude and the reaction is…
This paper investigates the propagation phenomena of a monotone bistable reaction-diffusion system in an exterior domain of R2. By constructing suitable sub- and supersolutions, we establish the existence and monotonicity of an entire…
We prove existence of and construct transition fronts for a class of reaction- diffusion equations with spatially inhomogeneous Fisher-KPP type reactions and non-local diffusion. Our approach is based on finding these solutions as…
We prove the existence and provide the asymptotics for non local fronts in homogeneous media.
Front dynamics modeled by a reaction-diffusion equation are studied under the influence of spatio-temporal structured noises. An effective deterministic model is analytical derived where the noise parameters, intensity, correlation time and…