Well-posedness of boundary-value problems for the linear Benjamin-Bona-Mahony equation
Vishal Vasan Bernard Deconinck
Discrete & Continuous Dynamical Systems - A 2013, 33(7): 3171-3188 doi: 10.3934/dcds.2013.33.3171
A new method due to Fokas for explicitly solving boundary-value problems for linear partial differential equations is extended to equations with mixed partial derivatives. The Benjamin-Bona-Mahony equation is used as an example: we consider the Robin problem for this equation posed both on the half line and on the finite interval. For specific cases of the Robin boundary conditions the boundary-value problem is found to be ill posed.
keywords: PDEs with mixed derivatives Fokas method.
Pressure beneath a traveling wave with constant vorticity
Vishal Vasan Katie Oliveras
Discrete & Continuous Dynamical Systems - A 2014, 34(8): 3219-3239 doi: 10.3934/dcds.2014.34.3219
The main focus of this paper is to derive a direct relationship between the surface of an inviscid traveling gravity wave in two dimensions, and the pressure at the bottom of the fluid without approximation, including the effects of constant vorticity. Using this relationship, we reconstruct both the pressure and streamlines throughout the fluid domain. We compare our numerical results with various analytical results (such as the bounds presented in [7-10])as well as known numerical results (see [16]).
keywords: surface gravity waves Euler's equations. free-boundary problem Water-waves constant vorticity

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