Displaying similar documents to “Index des tomes LI-LXX (1990-1998)”

Vortex motion and phase-vortex interaction in dissipative Ginzburg-Landau dynamics

F. Bethuel, G. Orlandi, D. Smets (2004)

Journées Équations aux dérivées partielles

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We discuss the asymptotics of the parabolic Ginzburg-Landau equation in dimension N ≥ 2 . Our only asumption on the initial datum is a natural energy bound. Compared to the case of “well-prepared” initial datum, this induces possible new energy modes which we analyze, and in particular their mutual interaction. The two dimensional case is qualitatively different and requires a separate treatment.

Propagation of singularities for the wave equation on manifolds with corners

András Vasy (2004-2005)

Séminaire Équations aux dérivées partielles

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In this talk we describe the propagation of 𝒞 ∞ and Sobolev singularities for the wave equation on 𝒞 ∞ manifolds with corners M equipped with a Riemannian metric g . That is, for X = M × ℝ t , P = D t 2 - Δ M , and u ∈ H loc 1 ( X ) solving P u = 0 with homogeneous Dirichlet or Neumann boundary conditions, we show that WF b ( u ) is a union of maximally extended generalized broken bicharacteristics. This result is a 𝒞 ∞ counterpart of Lebeau’s results for the propagation of analytic singularities on real analytic manifolds with appropriately stratified...