相关论文: Self-sustaining traveling fronts for a model relat…

In this work, we study the propagation of wildfires using an advection--diffusion--reaction model which also includes convective and radiative heat loss. An existing model is discussed \cite{asensio_2002} and a physically consistent…

In this paper, we focus on the existence of propagation fronts, solutions to non-local dispersion reaction models. Our aim is to provide a unified proof of this existence in a very broad framework using simple real analysis tools. In…

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…

In a recent paper, we have introduced a new model to describe front propagation in bushfires. This model describes temperature diffusion in view of an ignition process induced by an interaction kernel, the effect of the environmental wind…

In this paper we consider a classical model of gasless combustion in a one dimensional formulation under the assumption of ignition temperature kinetics. We study the propagation of flame fronts in this model when the initial distribution…

We consider the propagation of a flame front in a solid periodic medium. The model is governed by a free boundary system in which the front's velocity depends on the temperature via a kinetic rate which may degenerate. We show the existence…

In this paper, we consider a reaction-diffusion system describing the propagation of flames under the assumption of ignition-temperature kinetics and fractional reaction order. It was shown in [3] that this system admits a traveling front…

For certain values of the wave speed parameter, evolution equations for the temperature of a region of fuel admit traveling wave solutions describing fire fronts. We consider such a system in the form of a nonlinear reaction-diffusion…

The current paper is devoted to the investigation of wave propagation phenomenon in reaction-diffusion equations with ignition type nonlinearity in time heterogeneous and random media. It is proven that such equations in time heterogeneous…

We prove the existence of a traveling wave solution for a boundary reaction diffusion equation when the reaction term is the combustion nonlinearity with ignition temperature. A key role in the proof is plaid by an explicit formula for…

Self-activation coupled to a transport mechanism results in traveling waves that describe polymerization reactions, forest fires, tumor growth, and even the spread of epidemics. Diffusion is a simple and commonly used model of particle…

This paper deals with the existence of traveling fronts guided by the medium for a KPP reaction-diffusion equation coming from a model in population dynamics in which there is spatial spreading as well as genetic mutation of a quantitative…

We investigate spreading properties of solutions of a large class of two-component reaction-diffusion systems, including prey-predator systems as a special case. By spreading properties we mean the long time behaviour of solution fronts…

Sufficient conditions for either existence or non-existence of traveling wave solutions for a general quasi-linear reaction-diffusion-convection equation, possibly highly degenerate or singular, with discontinuous coefficients are…

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…

We study traveling waves in a coordinate-free model of flame fronts. The flame front is the interface between the burnt and unburnt phases of a gas undergoing combustion. The front therefore moves in a preferred direction, as the unburnt…

We prove the existence and uniqueness, up to a shift in time, of curved traveling fronts for a reaction-advection-diffusion equation with a combustion-type nonlinearity. The advection is through a shear flow $q$. This analyzes, for…

In this paper, we study the existence of traveling wave solutions and the spreading speed for the solutions of an age-structured epidemic model with nonlocal diffusion. Our proofs make use of the comparison principles both to construct…

We provide a mathematical analysis of a thermo-diffusive combustion model of lean spray flames, for which we prove the existence of travelling waves. In the high activation energy singular limit we show the existence of two distinct…

We consider a free boundary model of epithelial cell migration with logistic growth and nonlinear diffusion induced by mechanical interactions. Using numerical simulations, phase plane and perturbation analysis, we find and analyse…