Geodesic
Variational Linear Problems in Wave--Obstacle Interaction
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximation theory, and nonlinear analysis, Tome 255 (2006), pp. 216-226

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We discuss the problem of the steady two-dimensional flow past fixed disturbances in an open channel of finite depth. We consider different types of obstacles: submerged or surface-piercing bodies and localized perturbations of a horizontal bottom. By a special variational approach, we prove the unique solvability of the linearized problem for supercritical velocities of the unperturbed flow. We also discuss extensions of the variational method to the limit case of a submerged beam and to subcritical velocities. 
@article{TM_2006_255_a15,
     author = {C. D. Pagani and D. Pierotti},
     title = {Variational {Linear} {Problems} in {Wave--Obstacle} {Interaction}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {216--226},
     publisher = {mathdoc},
     volume = {255},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2006_255_a15/}
}
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C. D. Pagani; D. Pierotti. Variational Linear Problems in Wave--Obstacle Interaction. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximation theory, and nonlinear analysis, Tome 255 (2006), pp. 216-226. http://geodesic.mathdoc.fr/item/TM_2006_255_a15/