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Alex Himonas: Analysis of water wave models

Submitted by Andreas L. Freund on March 3, 2016 - 11:00am

Speaker: Alex Himonas, University of Notre Dame

Date: March 3, 2016

Title: Analysis of water wave models

Abstract: Over the last two centuries several models have been proposed for describing the motion of shallow water waves and the phenomenon of their breaking and peaking. These models include the Korteweg-deVries, the Whitham and the Camassa-Holm equations. This talk will present the analysis of their initial value problem in low (Sobolev) and high (analytic) regularity data spaces. Also, it will present the analysis of the initial-boundary value problem for the Korteweg-deVries equation with data in Sobolev spaces using the unified transform method. The talk is based on work with A. Fokas, C. Holliman, C. Kenig, D. Mantzavinos, G. Misiolek, G. Petronilho, and G. Ponce.