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SUMMARY:Water waves: Theory\, computations and applications - Dimitrios Mi
 tsotakis (Victoria University of Wellington)
DTSTART:20221116T153000Z
DTEND:20221116T163000Z
UID:TALK192803@talks.cam.ac.uk
DESCRIPTION:Surface water waves of significant interest such as tsunamis\,
  solitary waves and undular bores are nonlinear and dispersive waves. Unlu
 ckily\, the equations describing the propagation of surface water waves kn
 own as Euler&rsquo\;s equations are immensely hard to solve. For this reas
 on\, several simplified systems of PDEs have been proposed as alternative 
 approximations to Euler&rsquo\;s equations. In this presentation we review
  the theoretical properties of such systems. We show that only some of the
  asymptotically derived systems obey to the laws of mathematics and physic
 s while there is only one with complete mathematical theory for physically
  sound initial-boundary value problems. We also discuss the numerical mode
 ling of such problems. In particular\, we focus on Galerkin / Finite eleme
 nt methods\, which is a class of high-order methods that has been proved c
 onvergent to certain initial-boundary value problems of physical interest 
 (perhaps the only one). We close this presentation with conditions for the
  existence of special solutions and validation with laboratory data.&nbsp\
 ;
LOCATION:Seminar Room 2\, Newton Institute
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