Related papers: Travelling wave mathematical analysis and efficien…
We study two mathematical descriptions of a charged particle interacting with it's self-generated electromagnetic field. The first model is the one-body Maxwell-Schr\"odinger system where the interaction of the spin with the magnetic field…
We consider an evolution equation of parabolic type in R having a travelling wave solution. We perform an appropriate change of variables which transforms the equation into a non local evolution one having a travelling wave solution with…
The simulation of turbulent combustion phenomena is still an open problem in modern fluid dynamics. Considering the economical importance of hydrocarbon combustion in energy production processes, it is evident the need of an accurate tool…
This paper is concerned with the traveling waves of delayed reaction-diffusion systems where the reaction function possesses the mixed quasimonotonicity property. By the so-called monotone iteration scheme and Schauder's fixed point…
In recent years, forest fires and maritime accidents have occurred frequently, which have had a bad impact on human production and life. Thus, the development of seaplanes is an increasingly urgent demand. It is important to study the…
We study travelling wave solutions of a 1D continuum model for collective cell migration in which cells are characterised by position and polarity. Four different types of travelling wave solutions are identified which represent…
A well-known optimal velocity (OV) model describes vehicle motion along a single lane road, which reduces to a perturbed modified Korteweg-de Vries (mKdV) equation within the unstable regime. Steady travelling wave solutions to this…
Traveling waves for the FPU chain are constructed by solving the associated equation for the spatial profile $u$ of the wave. We consider solutions whose derivatives $u'$ need not be small, may change sign several times, but decrease at…
In the dynamics generated by the suspension bridge equation, traveling waves are an essential feature. The existing literature focuses primarily on the idealized one-dimensional case, while traveling structures in two spatial dimensions…
In this paper, we study the traveling wave solutions to the density-suppressed motility model describing the ``self-trapping'' mechanism that induces spatio-temporal pattern formations observed in the experiment. We establish the existence…
We use a geometric approach to prove the existence of smooth travelling wave solutions of a nonlinear diffusion-reaction equation with logistic kinetics and a convex nonlinear diffusivity function which changes sign twice in our domain of…
The present paper is concerned with the existence of traveling wave solutions of the asymptotic model, derived by the authors in a previous work, to approximate the unidirectional evolution of a collision-free plasma in a magnetic field.…
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…
Steady propagation of premixed flames in straight channels is studied numerically using the on-shell approach. A first numerical algorithm for solving the system of nonlinear integro-differential on-shell equations is presented. It is based…
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 numerically study nonlinear phenomena related to the dynamics of traveling wave solutions of the Serre equations including the stability, the persistence, the interactions and the breaking of solitary waves. The numerical method utilizes…
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…
A new premixed turbulent combustion model is proposed. It is based on one-dimensional (1D) filtering of density times progress variable and of the reaction source term of laminar premixed flame profiles using a filter kernel which reflects…
The Fisher-KPP model, and generalisations thereof, is a simple reaction-diffusion models of biological invasion that assumes individuals in the population undergo linear diffusion with diffusivity $D$, and logistic proliferation with rate…
In this paper the travelling wave solutions in the adiabatic model with two-step chain branching reaction mechanism are investigated both numerically and analytically in the limit of equal diffusivity of reactant, radicals and heat. The…