Related papers: Super-linear spreading in local and non-local cane…
The spreading of evolutionary novelties across populations is the central element of adaptation. Unless population are well-mixed (like bacteria in a shaken test tube), the spreading dynamics not only depends on fitness differences but also…
A mutualist model with nonlocal diffusions and a free boundary is first considered. We prove that this problem has a unique solution defined $t\ge0$, and its dynamics are governed by a spreading-vanishing dichotomy. Some criteria for…
Non-linear sound propagation is investigated computationally by simulating compressible time-developing mixing layers using the Large Eddy Simulation (LES) approach and solving the viscous Burgers Equation. The mixing layers are of…
In this paper, we proceed to study the nonlocal diffusion problem proposed by Li and Wang [8], where the left boundary is fixed, while the right boundary is a nonlocal free boundary. We first give some accurate estimates on the longtime…
In this paper, we study the existence and stability of travelling wave solutions of a kinetic reaction-transport equation. The model describes particles moving according to a velocity-jump process, and proliferating thanks to a reaction…
The aim of this paper is to provide a comprehensive study of some linear nonlocal diffusion problems in metric measure spaces. These include, for example, open subsets in $\mathbb{R}^N$, graphs, manifolds, multi-structures or some fractal…
The system under study is a reaction-diffusion equation in a horizontal strip, coupled to a diffusion equation on its upper boundary via an exchange condition of the Robin type. This class of models was introduced by H. Berestycki, L. Rossi…
UK woodlands, forests, and urban treescapes are under threat from invasive species, exacerbated by climate change, trade, and transport. Invasive tree pests debilitate their host and disrupt forest ecosystems, thus it is imperative to…
Localization-delocalization transition in a discrete Anderson nonlinear Schr\"odinger equation with disorder is shown to be a critical phenomenon $-$ similar to a percolation transition on a disordered lattice, with the nonlinearity…
The source term in a reaction-diffusion system, in general, does not involve explicit time dependence. A class of self-limiting growth models dealing with animal and tumor growth and bacterial population in a culture, on the other hand are…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
We consider semilinear evolution equations of the form $a(t)\partial_{tt}u + b(t) \partial_t u + Lu = f(x,u)$ and $b(t) \partial_t u + Lu = f(x,u),$ with possibly unbounded $a(t)$ and possibly sign-changing damping coefficient $b(t)$, and…
Linear elastic fracture mechanics theory predicts that the speed of crack growth is limited by the Rayleigh wave speed. Although many experimental observations and numerical simulations have supported this prediction, some exceptions have…
In this paper we provide explicit description of the pinning region and propagation reversal phenomenon for the bistable reaction diffusion equation on regular biinfinite trees. In contrast to the general existence results for smooth…
Anomalous dynamics in which local perturbations spread faster than diffusion are ubiquitously observed in the long-time behavior of a wide variety of systems. Here, the manner by which such systems evolve towards their asymptotic…
We present a model for diffusion in a molecularly crowded environment. The model consists of random barriers in percolation network. Random walks in the presence of slowly moving barriers show normal diffusion for long times, but anomalous…
We study front propagation phenomena for a large class of nonlocal KPP-type reaction-diffusion equations in oscillatory environments, which model various forms of population growth with periodic dependence. The nonlocal diffusion is an…
We study the existence and uniqueness of mild and strong solutions of nonlocal nonlinear diffusion problems of $p$-Laplacian type with nonlinear boundary conditions posed in metric random walk spaces. These spaces include, among others,…
Cell proliferation and diffusion can be modeled through reaction-diffusion systems describing the space-time evolution of a density variable. In this work, we present non-linear transformations of heat equation solutions to model cellular…
This paper is concerned with the large-time dynamics of bounded solutions of reaction-diffusion equations with bounded or unbounded initial support in R N. We start with a survey of some old and recent results on the spreading speeds of the…