Related papers: Acceleration or finite speed propagation in weakly…
The propagation of nonlinear waves in one dimensional space, unsteady and compressible flow in Darcy-type porous media is analyzed. It is assumed that the weak discontinuity propagate long the characteristic path using the characteristics…
We study the existence and uniqueness of wavefronts to the scalar reaction-diffusion equations $u_{t}(t,x) = \Delta u(t,x) - u(t,x) + g(u(t-h,x)),$ with monotone delayed reaction term $g: \R_+ \to \R_+$ and $h >0$. We are mostly interested…
A stress-affected chemical reaction front propagation is considered utilizing the concept of a chemical affinity tensor. A reaction between an elastic solid and diffusing constituents, localized at the reaction front, is considered. As a…
This work focuses on dynamics arising from reaction-diffusion equations , where the profile of propagation is no longer characterized by a single front, but by a layer of several fronts which we call a propagating terrace. This means,…
We survey recent results on reaction-diffusion equations with discontinuous hysteretic nonlinearities. We connect these equations with free boundary problems and introduce a related notion of spatial transversality for initial data and…
For one dimensional homogeneous bistable diffusion equations, Fife-McLeod ([Arch. Ration. Mech. Anal., 65 (1977), 335-361]) gave a well-known theorem which says that spreading solutions starting from compactly supported initial data can be…
Reaction-diffusion processes in two-dimensional percolating structures are investigated. Two different problems are addressed: reaction spreading on a percolating cluster and front propagation through a percolating channel. For reaction…
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…
We study non-relativistic propagation of Gaussian wave packets in one-dimensional Eckart potential, a barrier, or a well. In the picture used, the transmitted wave packet results from interference between the copies of the freely…
We are interested in the threshold phenomena for propagation in nonlocal diffusion equations with some compactly supported initial data. In the so-called bistable and ignition cases, we provide the first quantitative estimates for such…
This paper is concerned with the asymptotic behavior of the generalized principal eigenvalues of elliptic operators and spreading speeds of Fisher-KPP equations in two-scale almost periodic media where one scale is fixed and another one…
Spreading of bacteria in a highly advective, disordered environment is examined. Predictions of super-diffusive spreading for a simplified reaction-diffusion equation are tested. Concentration profiles display anomalous growth and…
We experimentally probe nonlinear wave propagation in weakly compressed granular media, and observe a crossover from quasi-linear sound waves at low impact, to shock waves at high impact. We show that this crossover grows with the confining…
We perform the analysis of a hyperbolic model which is the analog of the Fisher-KPP equation. This model accounts for particles that move at maximal speed $\epsilon^{-1}$ ($\epsilon\textgreater{}0$), and proliferate according to a reaction…
We consider a reaction-diffusion system for two densities lying in adjacent domains of $\mathbb{R}^N$. We treat two configurations: either a cylinder and its complement, or two half-spaces. Diffusion and reaction heterogeneities for the two…
We consider the homogeneous integro-differential equation$\partial \_t u=J*u-u+f(u)$ with a monostable nonlinearity $f$. Our interest is twofold: we investigate the existence/non existence of travelling waves, and the propagation properties…
The long-time behavior of a reaction-diffusion front between one static (e.g. porous solid) reactant A and one initially separated diffusing reactant B is analyzed for the mean-field reaction-rate density R(\rho_A,\rho_B) =…
We consider a monostable time-delayed reaction-diffusion equation arising from population dynamics models. We let a small parameter tend to zero and investigate the behavior of the solutions. We construct accurate lower barriers --- by…
The nonlocal Fisher equation is a diffusion-reaction equation with a nonlocal quadratic competition, which describes the reaction between distant individuals. This equation arises in evolutionary biological systems, where the arena for the…
We investigate the propagation of initial value perturbations along the solution of a linear ordinary differential equation \( y'(t) = Ay(t) \). This propagation is analyzed using the relative error rather than the absolute error. Our focus…