Water wave propagation phenomena still attract the interest of researchers from many areas and with various objectives, including better experimental, physical and mathematical understanding of their dynamics, especially in near-shore zones, harnessing their power, improvement of the accuracy of wave field observations, risk assessment and development of emergency plans to prevent damage due to extreme phenomena like storm waves and tsunamis, etc. All objectives depend on a better mathematical description of the waves and their properties.

The mathematical modelling of wave propagation, either on the surface of a fluid or on the interface of immiscible fluid layers of different densities, is based in the simplest case on the Euler equations for irrotational waves in the relevant physical setting. In many applications, the full Euler equations are too complex to allow a detailed study of the dynamics of the problem, and the derivation of simpler, approximate partial differential equation (pde) models in various scaling regimes, is in order. The validity of these models as approximations of the Euler equations, their rigorous mathematical analysis, the study of their special solutions such as solitary waves, the construction and error analysis of efficient numerical methods for the simulation of their solutions, and the comparison of numerical predictions with experimental results are still challenging topics of intensive research.

The purpose of this workshop is to present modern aspects of the validity, pde theory and numerical analysis of such models of surface or internal water waves, that are usually represented by systems of nonlinear, dispersive wave equations and related hyperbolic equations. Internationally known researchers, mathematicians, physicists and engineers will be invited to attend, interact, and present their latest work in the area. The workshop will also have a strong training component as several young researchers (PhD candidates) working in the general area of nonlinear waves, will be invited to present their results and problems.

SCHEDULE

MONDAY 27

MORNING
9-9:30 Opening
9:30-10:15 J. Bona: ‘Systems of equations for internal waves’.
10:15-11:00 B. Cano: ‘How to avoid order reduction when Lawson
methods integrate nonlinear initial boundary value problems’.
11:00-11:30 Coffee break
11:30-12:15 O. Karakashian: ‘Finite Element Methods for a system of
Dispersive Equations’.
12:30-13:15 D. Pelinovsky: ‘Convergence of Petviashvili's method near
periodic waves’.
Chairman: A. Durán.

13:15 Lunch Hotel Las Rocas

AFTERNOON
15:30-16:15 H. Chen: ‘Stability and instability of solitary-wave solutions
to coupled systems of nonlinear dispersive equations’.
16:30-17:15 T. Katsaounis: ‘Galerkin finite element methods for
Boussinesq-Peregrine type systems’.
17:30-18:15 R. Granero: ‘Asymptotic models for free boundaries in
incompressible flows’.
Chairman: B. Cano.

TUESDAY 28

MORNING
9-9:45 V. A. Dougalis: ‘Galerkin-finite element methods for the Camassa-
Holm equation’.
10:00-10:45 R. Barros: ‘Large amplitude mode-2 internal solitary waves
in three-layer flows’.
11:00-11:30 Coffee break
11:30-12:15 M. J. Castro: ‘Modeling tsunamis generated by submerged
landslides in shallow-flows’.
12:30-13:15 E. Dinvay: ‘Whitham--Boussinesq models: well-posedness
and numerical simulation’.
Chairman: T. Katsaounis.

13:15 Lunch Hotel Las Rocas

AFTERNOON
15:30-16:15 J.-C. Saut: ‘On some internal waves systems’.
16:30-17:15 A. Durán: ‘On solitary wave solutions of Boussinesq-Full
dispersion systems for internal waves’.
Chairman: V. A. Dougalis.

WEDNESDAY 29
MORNING
Special session for graduate students
9:00-9:30 G. Kounadis: ‘Galerkin methods for the Classical Boussinesq
system over a variable bottom’.
9:30-10:00 L. Saridaki: ‘Error estimates for spectral semidiscretizations of
Boussinesq systems’.
10:00-10:30 D. Bolbot: ‘Diffusive-dispersive travelling wave solutions’.
10:30-11:00 Coffee break.
11:00-12:00 Final conference:
Alberto Peña Bandrés (UPV): ‘Experimental validation of a CFD model
using a narrow wave flume’.
Chairman: A. Durán

13:15 Lunch Hotel Las Rocas