Homogenization of degenerate second-order PDE in periodic and almost periodic environments and applications
Asymmetric potentials and motor effect : a homogenization approach
PDE-viscosity solution approach to some problems of large deviations
Équations aux dérivées partielles stochastiques nonlinéaires et solutions de viscosité
The relation between the porous medium and the eikonal equations in several space dimensions.
We study the relation between the porous medium equation ut = Δ(um), m > 1, and the eikonal equation vt = |Dv|2. Under quite general assumtions, we prove that the pressure and the interface of the solution of the Cauchy problem for the porous medium equation converge as m↓1 to the viscosity solution and the interface of the Cauchy problem for the eikonal equation. We also address the same questions...
Stochastic averaging lemmas for kinetic equations
We develop a class of averaging lemmas for stochastic kinetic equations. The velocity is multiplied by a white noise which produces a remarkable change in time scale. Compared to the deterministic case and as far as we work in , the nature of regularity on averages is not changed in this stochastic kinetic equation and stays in the range of fractional Sobolev spaces at the price of an additional expectation. However all the exponents are changed; either time decay rates are slower (when...
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