Displaying similar documents to “Almost global solutions for non hamiltonian semi-linear Klein-Gordon equations on compact revolution hypersurfaces”

On the uniqueness of ground states of non-local equations

Rupert L. Frank (2011)

Journées Équations aux dérivées partielles

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We review our joint result with E. Lenzmann about the uniqueness of ground state solutions of non-linear equations involving the fractional Laplacian and provide an alternate uniqueness proof for an equation related to the intermediate long-wave equation.

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,...

Expansions and eigenfrequencies for damped wave equations

Michael Hitrik (2001)

Journées équations aux dérivées partielles

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We study eigenfrequencies and propagator expansions for damped wave equations on compact manifolds. In the strongly damped case, the propagator is shown to admit an expansion in terms of the finitely many eigenmodes near the real axis, with an error exponentially decaying in time. In the presence of an elliptic closed geodesic not meeting the support of the damping coefficient, we show that there exists a sequence of eigenfrequencies converging rapidly to the real axis. In the case of...

Spectral properties of non-self-adjoint operators

Johannes Sjöstrand (2009)

Journées Équations aux dérivées partielles

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This text contains a slightly expanded version of my 6 hour mini-course at the PDE-meeting in Évian-les-Bains in June 2009. The first part gives some old and recent results on non-self-adjoint differential operators. The second part is devoted to recent results about Weyl distribution of eigenvalues of elliptic operators with small random perturbations. Part III, in collaboration with B. Helffer, gives explicit estimates in the Gearhardt-Prüss theorem for semi-groups.