Related papers: Variational Approach of Critical Sharp Front Speed…
Invasion fronts in ecology are well studied but very few mathematical results concern the case with variable motility (possibly due to mutations). Based on an apparently simple reaction-diffusion equation, we explain the observed phenomena…
Most biochemical reactions in living cells rely on diffusive search for target molecules or regions in a heterogeneous overcrowded cytoplasmic medium. Rapid re-arrangements of the medium constantly change the effective diffusivity felt…
In this paper, we deal with models with Born-Infeld type diffusion and monostable reaction, investigating the effect of the introduction of a convection term on the limit shape of the critical front profile for vanishing diffusion. We first…
We study multiplicity of the supercritical traveling front solutions for scalar reaction-diffusion equations in infinite cylinders which invade a linearly unstable equilibrium. These equations are known to possess traveling wave solutions…
In the present work, the discrete flame model [1] is augmented by introducing the thermal inertia of particles in the preheating zone. The effect of particle thermal inertia on flame speed, propagation limits, and near-limits dynamics of…
Diffusion models have achieved state-of-the-art performance in generating many different kinds of data, including images, text, and videos. Despite their success, there has been limited research on how the underlying diffusion process and…
We give an explicit formula for the change of speed of pushed and bistable fronts of the reaction diffusion equation when a small cutoff is applied at the unstable or metastable equilibrium point. The results are valid for arbitrary…
We develop theory to understand an intriguing property of diffusion models for image generation that we term critical windows. Empirically, it has been observed that there are narrow time intervals in sampling during which particular…
We analyze the emergence of diffractive focusing in the transition from discrete to continuous space-time variables. Three types of dynamical equations are studied in a top-to-bottom approach, starting with the most general system. First we…
We consider a solution $u(\cdot,t)$ to an initial boundary value problem for time-fractional diffusion-wave equation with the order $\alpha \in (0,2) \setminus \{ 1\}$ where $t$ is a time variable. We first prove that a suitable norm of…
We study the long time behavior (homogenization) of a diffusion in random medium with time and space dependent coefficients. The diffusion coefficient may degenerate. In Stochastic Process. Appl. (2007) (to appear), an invariance principle…
We investigated the propagation of turbulent fronts in pipe flow at high Reynolds numbers by direct numerical simulation. We used a technique combining a moving frame of reference and an artificial damping to isolate the fronts in short…
We show the existence of traveling front solutions in a diffusive classical SIS epidemic model and the SIS model with a saturating incidence in the size of the susceptible population. We investigate the situation where both susceptible and…
In this paper, a fractional generalization of the wave equation that describes propagation of damped waves is considered. In contrast to the fractional diffusion-wave equation, the fractional wave equation contains fractional derivatives of…
We revisit the nonlinear stability of the critical invasion front in the Ginzburg-Landau equation. Our main result shows that the amplitude of localized perturbations decays with rate $t^{-3/2}$, while the phase decays diffusively. We…
A study of a stable front propagating in a turbulent medium is presented. The front is generated through a reaction-diffusion equation, and the turbulent medium is statistically modeled using a Langevin equation. Numerical simulations…
A modified method of functional constraints is used to construct the exact solutions of nonlinear equations of reaction-diffusion type with delay and which are associated with variable coefficients. This study considers a most generalized…
The problem of velocity selection for reaction fronts has been intensively investigated, leading to the successful marginal stability approach for propagation into an unstable state. Because the front velocity is controlled by the leading…
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 parabolic models. Emphasis is given toward the numerical…
We analyze experimentally chemical waves propagation in the disordered flow field of a porous medium. The reaction fronts travel at a constant velocity which drastically depends on the mean flow direction and rate. The fronts may propagate…