Related papers: Propagation in a non local reaction diffusion equa…
A new asymptotic method is presented for the analysis of the traveling waves in the one-dimensional reaction-diffusion system with the diffusion with a finite velocity and Kolmogorov-Petrovskii-Piskunov kinetics. The analysis makes use of…
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…
We show that propagation speeds in invasion processes modeled by reaction-diffusion systems are determined by marginal spectral stability conditions, as predicted by the marginal stability conjecture. This conjecture was recently settled in…
This paper is devoted to the study of the asymptotic behaviors of the minimal speed of propagation of pulsating traveling fronts solving the Fisher-KPP reaction-advection-diffusion equation within either a large drift, a mixture of large…
In this paper, we study propagation in a nonlocal reaction-diffusion-mutation model describing the invasion of cane toads in Australia. The population of toads is structured by a space variable and a phenotypical trait and the…
In this paper, we study the large time behaviour of solutions of multistable reaction-diffusion equations in $\mathbb{R}^N$, with a spatially periodic heterogeneity. By multistable, we mean that the problem admits a finite -- but…
These notes are based on the lectures given in a mini-course at VIASM (Vietnam Institute for Advanced Study in Mathematics) 2025 Summer School. They give a brief account of the theory (with detailed proofs) for propagation governed by a…
In this paper we focus on three problems about the spreading speeds of nonlocal dispersal Fisher-KPP equations. First, we study the signs of spreading speeds and find that they are determined by the asymmetry level of the nonlocal dispersal…
We study reaction-diffusion systems where diffusion is by jumps whose sizes are distributed exponentially. We first study the Fisher-like problem of propagation of a front into an unstable state, as typified by the A+B $\to$ 2A reaction. We…
Understanding anomalous transport and reaction kinetics due to microscopic physical and chemical disorder is a long-standing goal in many fields including geophysics, biology, and engineering. We consider reaction-diffusion characterized by…
We address the problem of a front propagation in chains with a bi-stable nondegenerate on-site potential and a nonlinear gradient coupling. For a generic nonlinear coupling, one encounters a special regime of transitions, characterized by…
The work proposes and studies a one-dimensional model, which involves nonlocal interactions and finite propagation speed. It shows that the general reaction-diffusion equation, the Swift-Hohenberg equation and the general…
We study the front propagation in Reaction-Diffusion systems whose reaction dynamics exhibits an unstable fixed point and chaotic or noisy behaviour. We have examined the influence of chaos and noise on the front propagation speed and on…
We study the propagation of singularities in solutions of linear convection equations with spatially heterogeneous nonlocal interactions. A spatially varying nonlocal horizon parameter is adopted in the model, which measures the range of…
In this paper, we propose a new mathematical model nonlinear reaction-diffusion PDE's describing the dynamics of propagation of cancer. Here the mixed problem for the proposed PDE's is investigated and by applying obtained results…
We study the diffusion (or heat) equation on a finite 1-dimensional spatial domain, but we replace one of the boundary conditions with a "nonlocal condition", through which we specify a weighted average of the solution over the spatial…
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 the time asymptotic propagation of solutions to the reaction-diffusion cooperative systems with fractional diffusion. We prove that the propagation speed is exponential in time, and we find the precise exponent of propagation. This…
This paper is concerned with the interaction between a planar traveling front and a compact obstacle for monotone bistable reaction-diffusion systems in exterior domains. By constructing appropriate sub- and supersolutions, we first…
We consider a reaction-diffusion equation with nonlocal anisotropic diffusion and a linear combination of local and nonlocal monostable-type reactions in a space of bounded functions on $\mathbb{R}^d$. Using the properties of the…