CRM: Centro De Giorgi
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Dispersive and subelliptic PDEs

On global attraction to the manifold of solitary waves

speaker: Andrew Comech (Texas A&M University)

abstract: The solitary resolution conjecture states that any finite energy solution asymptotically is a superposition of outgoing solitary waves and the dispersive wave. While there is no proof of this general statement, we prove the following two results: (1) Any global finite energy solution to a generic nonlinear Klein-Gordon equation which is assumed to have compact spectrum (the support of the Fourier transform in time) converges to the set of solitary waves; (2) Any global finite energy solution to the Klein-Gordon equation with the nonlinearity on the compact part of a hypersurface indeed has compact spectrum, and consequently converges to the set of solitary waves. The proof is based on the Titchmarsh convolution theorem and its version for the partial convolution.

Wed 12 Feb, 9:20 - 10:10, Aula Dini


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