Related papers: Spreading speeds for one-dimensional monostable re…
This paper concerns the spreading speed and asymptotical behaviors, which was left as an open problem in \cite{LLW22}, of a Fisher-KPP nonlocal diffusion model with a free boundary. Using a new lower solution, we get the exact finite…
We study the minimal speed of propagating fronts of convection reaction diffusion equations of the form $u_t + \mu \phi(u) u_x = u_{xx} +f(u)$ for positive reaction terms with $f'(0 >0$. The function $\phi(u)$ is continuous and vanishes at…
This paper studies the phenomenon of invasion for heterogeneous reaction-diffusion equations in periodic domains with monostable and combustion reaction terms. We give an answer to a question rised by Berestycki, Hamel and Nadirashvili in…
In this paper we investigate the dynamical properties of a spatially periodic reaction-diffusion system {whose reaction terms are of hybrid nature in the sense that they are partly competitive and partly cooperative depending on the value…
We investigate multidimensional model for incompressible non-Newtonian fluids. Using method of energy estimates we prove the property of finite speed of propagations of the solution support for this problem. We find sharp bounds of the…
We study the propagation properties of the solutions of the finite-difference space semi-discrete wave equation on an uniform grid of the whole Euclidean space. We provide a construction of high frequency wave packets that propagate along…
We investigate velocity statistics of homogeneous inelastic gases using the Boltzmann equation. Employing an approximate uniform collision rate, we obtain analytic results valid in arbitrary dimension. In the freely evolving case, the…
In this paper, we study univariate and planar random motions with variable propagation speeds. We first consider motions with space-varying velocity, which can be reduced to constant-velocity motions by means of suitable nonlinear…
We consider solutions in frequency bands of dispersive equations on the line defined by Fourier multipliers, these solutions being considered as wave packets. In this paper, a refinement of an existing method permitting to expand…
Using spatial domain techniques developed by the authors and Myunghyun Oh in the context of parabolic conservation laws, we establish under a natural set of spectral stability conditions nonlinear asymptotic stability with decay at Gaussian…
We show, for some classes of diffusion coefficients that, generically in f, all equilibria of the reaction-diffusion equation u_t = (a(x)u_x)_x + f(u) with homogeneous Neumann boundary conditions are hyperbolic.
The present paper is devoted to the study of transition fronts in nonlocal reaction-diffusion equations with time heterogeneous nonlinearity of ignition type. It is proven that such an equation admits space monotone transition fronts with…
We propose a phase-space formulation for the nonlinear Schr\"odinger equation with a white-noise potential in order to shed light on two issues: the rate of spread and the singularity formation in the average sense. Our main tools are the…
We study acceleration phenomena in monostable integro-differential equations with ignition nonlinearity. Our results cover fractional Laplace operators and standard convolutions in a unified way, which is also a contribution of this paper.…
We study the asymptotic stability of traveling fronts and front's velocity selection problem for the time-delayed monostable equation $(*)$ $u_{t}(t,x) = u_{xx}(t,x) - u(t,x) + g(u(t-h,x)),\ x \in \mathbb{R},\ t >0$, considered with…
The late-time distribution function P(x,t) of a particle diffusing in a one-dimensional logarithmic potential is calculated for arbitrary initial conditions. We find a scaling solution with three surprising features: (i) the solution is…
Blow-up rates are established for general solutions to the quasilinear diffusion equation $$ \partial_tu=\Delta u^m+|x|^{\sigma}u^p, \quad (x,t)\in\mathbb{R}^N\times(0,T), $$ in the range of exponents $1<p<m$, $\sigma>0$. More precisely, if…
This paper is devoted to the analysis of the large-time behavior of solutions of one-dimensional Fisher-KPP reaction-diffusion equations. The initial conditions are assumed to be globally front-like and to decay at infinity towards the…
We consider a class of nonlinear Boltzmann equations describing return to thermal equilibrium in a gas of colliding particles suspended in a thermal medium. We study solutions in the space $L^{1}(\mathbb{R}^{3}\times \mathbb{T}^3).$ Special…
This paper is devoted to the study of propagation phenomena for a Lotka-Volterra reaction-advection-diffusion competition model in a periodic habitat. We first investigate the global attractivity of a semi-trival steady state for the…