1:00 pm Wednesday, September 29, 2010
Analysis Seminar: Nonlinear Klein-Gordon equation in discrete space-time: well-posedness, energy and charge conservation, and global attractors by
Andrew Comech (Texas A & M) in RLM 10.176
We consider the U(1)-invariant Klein-Gordon equation in discrete space-time, with the nonlinearity concentrated at one point. We show that solitary waves form the weak global attractor for this equation. That is, for large positive or negative times any finite energy solution converges to the set of all solitary waves. The convergence takes place in localized (weighted) norms. Important points in the proof are the Titchmarsh convolution theorem for functions supported on a circle and the existence theory for the nonlinear Klein-Gordon equation in discrete space-time. This is a joint work with Alexander Komech, Vienna University and IITP, Moscow. Submitted by
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