Andrej Zlatos

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We obtain a criterion for pulsating front speed-up by general periodic incompressible flows in two dimensions and in the presence of KPP nonlinearities. We achieve this by showing that the ratio of the minimal front speed and the effective diffusivity of the flow is bounded away from zero and infinity by constants independent of the flow. We also study(More)
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-front-type global in time solutions while creating a global in time bump-like solution. This is the first example of a medium in which no reaction-diffusion(More)
Abstract. We construct non-random bounded discrete half-line Schrödinger operators which have purely singular continuous spectral measures with fractional Hausdorff dimension (in some interval of energies). To do this we use suitable sparse potentials. Our results also apply to whole line operators, as well as to certain random operators. In the latter case(More)
We consider the advection-diffusion equation φt +Au · ∇φ = ∆φ, φ(0, x) = φ0(x) on R, with u a periodic incompressible flow and A 1 its amplitude. We provide a sharp characterization of all u that optimally enhance dissipation in the sense that for any initial datum φ0 ∈ L(R), p <∞, and any τ > 0, ‖φ(·, τ)‖∞ → 0 as A→∞. Our characterization is expressed in(More)