Existence of travelling-wave solutions and local well-posedness of the Fowler equation
Borys Alvarez-Samaniego Pascal Azerad
Discrete & Continuous Dynamical Systems - B 2009, 12(4): 671-692 doi: 10.3934/dcdsb.2009.12.671
We study the existence of travelling-waves and local well-posedness in a subspace of $C_b^1(\R)$ for a nonlinear evolution equation recently proposed by Andrew C. Fowler to describe the dynamics of dunes. The travelling-waves we obtained however, were more bore-like than solitary-wave-like.
keywords: travelling-wave. Nonlocal evolution equation
Low complexity shape optimization & a posteriori high fidelity validation
Afaf Bouharguane Pascal Azerad Frédéric Bouchette Fabien Marche Bijan Mohammadi
Discrete & Continuous Dynamical Systems - B 2010, 13(4): 759-772 doi: 10.3934/dcdsb.2010.13.759
In this paper, shape optimization tools are applied to coastal engineering. A barred beach protection study is described, using a new type of water wave attenuator device, namely geotextile tube, to reduce the mobilization of sediments. A global optimization algorithm, able to pursue beyond local minima, is used to search for the optimum properties of the geotextile tube.The optimal configuration is then post-validated for generated currents.
keywords: geotube coastal engineering. water wave propagation circulation Shape optimization

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