Related papers: Exact Propagating Wave Solutions in Reaction Cross…
We investigate travelling wave solutions in reaction-diffusion models of animal range expansion in the case that population diffusion is density-dependent. We find that the speed of the selected wave depends critically on the strength of…
Using a matrix product method the steady-state of a family of disordered reaction-diffusion systems consisting of different species of interacting classical particles moving on a lattice with periodic boundary conditions is studied. A new…
In this paper, we investigate the location of the spreading front and convergence to traveling wave profile of solutions to the Fisher-KPP equation in the following two cases: (i) in unbounded domains with an expanding boundary; (ii) on the…
We investigate a fast-reaction--diffusion system modelling the effect of autotoxicity on plant-growth dynamics, in which the fast-reaction terms are based on the dichotomy between healthy and exposed roots depending on the toxicity. The…
This paper is concerned with non-cooperative parabolic reaction--diffusion systems which share structural similarities with the scalar Fisher--KPP equation. These similarities make it possible to prove, among other results, an extinction…
We give sufficient conditions for the existence of positive travelling wave solutions for multi-dimensional autonomous reaction-diffusion systems with distributed delay. To prove the existence of travelling waves, we give an abstract…
We consider reaction-diffusion equations of KPP type in a presence of a line of fast diffusion with non-local exchange terms between the line and the framework. Our study deals with the infimum of the spreading speed depending on the…
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 introduce here a simple finite-dimensional feedback control scheme for stabilizing solutions of infinite-dimensional dissipative evolution equations, such as reaction-diffusion systems, the Navier-Stokes equations and the…
An analysis of traveling wave solutions of pure cross-diffusion systems, i.e., systems that lack reaction and self-diffusion terms, is presented. Using the qualitative theory of phase plane analysis the conditions for existence of different…
We investigate front propagation in a reacting particle system in which particles perform scale-free random walks known as Levy flights. The system is described by a fractional generalization of a reaction-diffusion equation. We focus on…
We examine numerically different zero-dimensional reaction-diffusion processes as candidate toy models for high-energy QCD evolution. Of the models examined -- Reggeon Field Theory, Directed Percolation and Reversible Processes -- only the…
A nonlinear reaction-diffusion system with cross-diffusion describing the COVID-19 outbreak is studied using the Lie symmetry method. A complete Lie symmetry classification is derived and it is shown that the system with correctly-specified…
We briefly review some aspects of the anomalous diffusion, and its relevance in reactive systems. In particular we consider {\it strong anomalous} diffusion characterized by the moment behaviour $\langle x(t)^q \rangle \sim t^{q \nu(q)}$,…
We study a two-species cross-diffusion model that is inspired by a system of convection-diffusion equations derived from an agent-based model on a two-dimensional discrete lattice. The latter model has been proposed to simulate gang…
The interaction of a Zeldovich reaction-diffusion front with a localized defect is studied numerically and analytically. For the analysis, we start from conservation laws and develop simple collective variable ordinary differential…
The aim of this paper is to study the generalized Fisher-KPP equation with nonlocal diffusion. In specific we prove the existence of a critical speed so that traveling front type solutions exist up to this critical speed and non-existence…
We discovered a new type of spiral wave solutions in reaction-diffusion systems --- spike spiral wave, which significantly differs from spiral waves observed in FitzHugh-Nagumo-type models. We present an asymptotic theory of these waves in…
This work deals with the position control of selected patterns in reaction-diffusion systems. Exemplarily, the Schl\"{o}gl and FitzHugh-Nagumo model are discussed using three different approaches. First, an analytical solution is proposed.…
The propagation of ON-OFF signals with dispersive waves is examined in this study. An integral-form exact solution for a simple ON-OFF switching event is derived, which holds for any dispersion relation. The integral can be exactly…