ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

10. Partial Differential Equations

1991 MS Classification: 35 Merzon, Anatoli, Moscow State Pedagogical University, Russia A complete solution of the Ursell problem We consider the problem of the description of all trapping modes associated with a plane sloping beach model. G. G. Stokes in 1846 and F. Ursell in 1952 had found M(α) trapping modes on a sloping beach of an angle α, where M(α) is the largest n for which (2n − 1)α ≤ π/2. However, it was not proved that all trapped modes in the Sobolev space H^{1} were obtained. We prove this conjecture. Part of these results is joint work with A. Komech and P. Zhevandrov. Reference: A. I. Komech, A. E. Merzon, P. N. Zhevandrov, On completeness of Ursell’s trapping modes. Russian Journal of Mathematical Physics, (4), nr. 4 (1996), 457-485.