Hypoelliptic estimates for some linear diffusive kinetic equations

Frédéric Hérau

Displaying similar documents to “Hypoelliptic estimates for some linear diffusive kinetic equations”

Isotropic hypoellipticity and trend to the equilibrium for the Fokker-Planck equation with high degree potential

Frédéric Hérau (2002)

Journées équations aux dérivées partielles

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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 well-posedness of the weak-Cauchy problem in both cases as well as instantaneous smoothing and exponential trend to equilibrium. Lower and upper bounds for the rate of convergence to equilibrium are obtained in terms of the lowest positive eigenvalue of the corresponding Witten laplacian,...

A mathematical aspect for Liesegang phenomena

Ohnishi, Isamu, Mimura, Masayasu

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Klein-Gordon type decay rates for wave equations with time-dependent coefficients

Michael Reissig, Karen Yagdjian (2000)

Banach Center Publications

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This work is concerned with the proof of $L_{p} - L_{q}$ decay estimates for solutions of the Cauchy problem for the Klein-Gordon type equation $u_{t t} - λ^{2} (t) b^{2} (t) (Δ u - m^{2} u) = 0$ . The coefficient consists of an increasing smooth function $λ$ and an oscillating smooth and bounded function b which are uniformly separated from zero. Moreover, $m^{2}$ is a positive constant. We study under which assumptions for λ and b one can expect as an essential part of the decay rate the classical Klein-Gordon decay rate n/2(1/p-1/q).

An algorithm for quantum propagation through electron level crossings.

Clotilde Fermanian Kammerer, Caroline Lasser (2005)

Journées Équations aux dérivées partielles

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Global existence for coupled Klein-Gordon equations with different speeds

Pierre Germain (2011)

Annales de l’institut Fourier

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Consider, in dimension 3, a system of coupled Klein-Gordon equations with different speeds, and an arbitrary quadratic nonlinearity. We show, for data which are small, smooth, and localized, that a global solution exists, and that it scatters. The proof relies on the space-time resonance approach; it turns out that the resonant structure of this equation has features which were not studied before, but which are generic in some sense.