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We study the qualitative properties of the generalized transition fronts for the reaction diffusion equations with the spatially inhomogeneous nonlinearity of the ignition type. We show that transitio...
For a class of one-dimensional reaction-diffusion equations, we establish the existence of generalized fronts, as recently defined by Berestycki and Hamel. We also prove uniform nondegeneracy estimate...
We prove the existence and give the asymptotic behavior of non local fronts in homogeneous media.
The method for recognition and monitoring of ULF electrotelluric signals with steep fronts is presented. The method is based on the multicomponent measurements of the geoelectric field and recognition...
The concept that ocean fronts are important features in oceanic biology has a long history, as noted by the quotations cited above. The example of a functional understanding of fronts provided by a co...
The interplay of physical and biogeochemical processes in the ocean can result in well-defined vertical gradients and maxima in biological properties. When these gradients and maxima exist near the se...
We consider the reactive Boussinesq equations in a slanted cylinder, with zero stress boundary conditions and arbitrary Rayleigh number. We show that the equations have non-planar traveling front solu...
We consider a model for the propagation of a subsonic detonation wave through a porous medium introduced by Sivashinsky [8]. We show that it admits travelling wave solutions that converge in the limit...
We consider a reaction-diffusion-advection equation with a nonlinearity of the KPP type in a cellular flow. We show that the minimal pulsating traveling front speed c∗(A) in a flow ofamplitude A...
We establish existence of travelling fronts in thermo-diffusive systems of the KPP type in a shear flow with an arbitrary Lewis number and a positive heat-loss at the boundary. We then prove that the ...
We study the qualitative properties of the generalized transition fronts for the reactiondiffusion equations with the spatially inhomogeneous nonlinearity of the ignition type. We show that transition...
We consider KPP-type systems in a cylinder with an arbitrary Lewis number (the ratio of thermal and material diffusivities) in the presence of a shear flow. We show that traveling fronts solutions exi...
We consider Fisher-KPP-type reaction-diffusion equations with spatially inhomogeneous reaction rates. We show that a sufficiently strong localized inhomogeneity may prevent existence of transition-fro...
We consider solutions of the KPP-type equations with a periodically varying reaction rate, and compactly supported initial data. It has been shown by Bramson [5, 6] in the case of the constant reactio...
Abstract: We consider, in a $D-$dimensional cylinder, a non--local evolution equation that describes the evolution of the local magnetization in a continuum limit of an Ising spin system with Kawasaki...

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