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19972026
most citedNetworks beyond pairwise interactions: structure and dynamics

1.6k citations

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Showing 2011 · math.APShow all

9 papers · 2 filters

math.AP2011

The Harnack inequality for a class of degenerate elliptic operators

Francois Hamel, Andrej Zlatos

We prove a Harnack inequality for distributional solutions to a type of degenerate elliptic PDEs in dimensions. The differential operators in question are related to the Kolmog…

math.AP2011

Speed-up of combustion fronts in shear flows

Francois Hamel, Andrej Zlatos

This paper is concerned with the analysis of speed-up of reaction-diffusion-advection traveling fronts in infinite cylinders with periodic boundary conditions. The advection is a s…

math.AP2011★ 16 cited

Maximal and minimal spreading speeds for reaction diffusion equations in nonperiodic slowly varying media

Jimmy Garnier, Thomas Giletti, Gregoire Nadin

This paper investigates the asymptotic behavior of the solutions of the Fisher-KPP equation in a heterogeneous medium, associated with…

math.AP2011★ 9 cited

Nonlinear equations for fractional Laplacians II: existence, uniqueness, and qualitative properties of solutions

Xavier Cabre, Yannick Sire

This paper, which is the follow-up to part I, concerns the equation in , with , where stands for the fractional Laplaci…

math.AP2011

Inside dynamics of pulled and pushed fronts

Jimmy Garnier, Thomas Giletti, Francois Hamel +1

We investigate the inside structure of one-dimensional reaction-diffusion traveling fronts. The reaction terms are of the monostable, bistable or ignition types. Assuming that the…

math.AP2011

Propagation of low regularity for solutions of nonlinear PDEs on a Riemannian manifold with a sub-Laplacian structure

Frédéric Bernicot, Yannick Sire

Following \cite{B2}, we introduce a notion of para-products associated to a semi-group. We do not use Fourier transform arguments and the background manifold is doubling, endowed w…