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Initial-boundary value problems for Boussinesq-type systems

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HY2W01 - Modulation theory and dispersive shock waves

Certain nonlinear approximations to the Euler equations of hydrodynamics in the weakly nonlinear and weakly dispersive waves regime will be discussed in the context of their associated initial-boundary value problems on the half-line and the finite interval. In particular, explicit solution formulae will be derived via the unified transform of Fokas for the 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-boundary value problem that describes the dynamics of water waves in a basin with wall- boundary conditions. Numerical experiments illustrating the effect of the boundary conditions on the reflection of solitary waves by a vertical wall will also be discussed. This is joint work with Dimitrios Mitsotakis.

This talk is part of the Isaac Newton Institute Seminar Series series.

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