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SUMMARY:Initial-boundary value problems for Boussinesq-type systems - Dion
 yssis Mantzavinos (University of Kansas)
DTSTART:20220714T140000Z
DTEND:20220714T143000Z
UID:TALK175889@talks.cam.ac.uk
DESCRIPTION:Certain nonlinear approximations to the Euler equations of hyd
 rodynamics in the weakly nonlinear and weakly dispersive waves regime will
  be discussed in the context of their associated initial-boundary value pr
 oblems on the half-line and the finite interval. In particular\, explicit 
 solution formulae will be derived via the unified transform of Fokas for t
 he linearizations of these Boussinesq-type systems in the case of nonzero 
 boundary conditions. Furthermore\, well-posedness will be established for 
 a certain regularization of these systems in the context of an initial-bou
 ndary value problem that describes the dynamics of water waves in a basin 
 with wall- boundary conditions. Numerical experiments illustrating the eff
 ect of the boundary conditions on the reflection of solitary waves by a ve
 rtical wall will also be discussed. This is joint work with Dimitrios Mits
 otakis.
LOCATION:Seminar Room 1\, Newton Institute
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