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- Frédéric Hérau
- 2002

We consider the Fokker-Planck equation with a confining or anti-confining potential which behaves at infinity like a possibly high degree homogeneous function. Hypoellipticity techniques provide the… (More)

In certain applications one is interested in the long-time behavior of systems described by a linear partial differential equation. For example, in kinetic equations one studies the decay to… (More)

Hypocoercivity and exponential time decay for the linear inhomogeneous relaxation Boltzmann equation

- Frédéric Hérau
- Asymptotic Analysis
- 2006

We consider an inhomogeneous linear Boltzmann equation, with an external confining potential. The collision operator is a simple relaxation toward a local Maxwellian, therefore without diffusion. We… (More)

Short and long time behavior of the Fokker-Planck equation in a confining potential and applications

- Frédéric Hérau
- 2008

We consider the linear Fokker-Planck equation in a confining potential in space dimension d ≥ 3. Using spectral methods, we prove bounds on the derivatives of the solution for short and long time,… (More)

- Virginie Bonnaillie-Noël, Marc Dambrine, Frédéric Hérau, Grégory Vial
- SIAM J. Math. Analysis
- 2010

Ventcel boundary conditions are second order differential conditions that appear in asymptotic models. Like Robin boundary conditions, they lead to wellposed variational problems under a sign… (More)

- Frédéric Hérau, KAREL PRAVDA-STAROV
- 2010

We establish global hypoelliptic estimates for linear Landau-type operators. Linear Landau-type equations are a class of inhomogeneous kinetic equations with anisotropic diffusion whose study is… (More)

We study a semiclassical random walk with respect to a probability measure with a finite number n0 of wells. We show that the associated operator has exactly n0 exponentially close to 1 eigenvalues… (More)

This paper is a survey of articles [5, 6, 8, 9, 12, 16, 17]. We are interested in the influence of small geometrical perturbations on the solution of elliptic problems. The cases of a single… (More)

— We prove a global existence result with initial data of low regularity, and prove the trend to the equilibrium for the Vlasov-Poisson-Fokker-Planck system with small non linear term but with a… (More)

- Frédéric Hérau
- 2005

We consider the non-linear VPFP system with a coulombian repulsive interaction potential and a generic confining potential in space dimension d ≥ 3. Using spectral and kinetic methods we prove the… (More)