The initial value problem for transient water waves

A note on the singularities in the theory of water waves with an inertial surface

“…This coincides with the expression obtained by Finkelstein [1] for e = 0. This potential exists for finite time only.…”

Initial surface disturbance on a shear current: The Cauchy-Poisson problem with a twist

“…By introducing boundaries and/or non-uniform depth, far more involved initial value problems may be studied as indeed they have been over the two centuries which have passed since the initial works [5][6][7][8][9] . Excellent reviews covering most of the classical literature up to the time of their publication are Lamb's classical text 10 and the famous review of Wehausen and Laitone 11 .…”

Control of Wave Energy Converters for Maximum Power Absorption with Time Domain Analysis

“…Applying Green's theorem over the transient free surface Green function derives the integral equation. It is possible to show that transient free surface Green's function satisfies the initial boundary value problem without a body [17]. Integrating Green's theorem in terms of time from -∞ to ∞ using the properties of transient free surface Green's function and potential theory, the integral equation for the source strength on the body surface may be written as in Kara [18].…”