Pushed fronts of monostable reaction-diffusion-advection equations

Uniqueness of monostable pulsating wave fronts for time periodic reaction-diffusion equations

Keywords: Reaction–diffusion equations Pulsating wave fronts KPP and monostable nonlinearities Uniqueness a b s t r a c t We establish the uniqueness of pulsating wave fronts for reaction–diffusion equations in time periodic media with monostable nonlinearities. For the Kolmogorov–Petrovsky– Piskunov (KPP) type nonlinearity, this result provides a complete classification of all types of KPP pul...

The influence of advection on the propagation of fronts in reaction-diffusion equations

Propagation of fronts is a phenomenon which plays a central role in a varied array of different fields. Front solutions in combustion represent propagating flames in particular in the setting of deflagrations in premixed gases (see e.g. [13, 68]). In physics and chemistry, more generally, propagating fronts describe phase transitions as a steady transformation taking place at a well defined vel...

Numerical Solution of Advection-Diffusion-Reaction Equations

Existence and stability of traveling wave fronts in reaction advection diffusion equations with nonlocal delay

This paper is concerned with the existence, uniqueness and globally asymptotic stability of traveling wave fronts in the quasi-monotone reaction advection diffusion equations with nonlocal delay. Under bistable assumption, we construct various pairs of superand subsolutions and employ the comparison principle and the squeezing technique to prove that the equation has a unique nondecreasing trav...

Multiple Scale Reaction-Diffusion-Advection Problems with Moving Fronts

In this work we discuss the further development of the general scheme of the asymptotic method of differential inequalities to investigate stability and motion of sharp internal layers (fronts) for nonlinear singularly perturbed parabolic equations, which are called in applications reaction-diffusion-advection equations. Our approach is illustrated for some new important cases of initial bounda...