Linear Water Waves: A Mathematical Approach

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Cambridge University Press, 11 juil. 2002 - 513 pages
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This book gives a self-contained and up-to-date account of mathematical results in the linear theory of water waves. The study of waves has many applications, including the prediction of behavior of floating bodies (ships, submarines, tension-leg platforms etc.), the calculation of wave-making resistance in naval architecture, and the description of wave patterns over bottom topography in geophysical hydrodynamics. The first section deals with time-harmonic waves. Three linear boundary value problems serve as the approximate mathematical models for these types of water waves. The next section uses a plethora of mathematical techniques in the investigation of these three problems. The techniques used in the book include integral equations based on Green's functions, various inequalities between the kinetic and potential energy and integral identities which are indispensable for proving the uniqueness theorems. The so-called inverse procedure is applied to constructing examples of non-uniqueness, usually referred to as 'trapped nodes.'
 

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Table des matières

Basic Theory of Surface Waves
1
Greens Functions
21
Submerged Obstacles
50
Semisubmerged Bodies I
99
Semisubmerged Bodies II
142
Horizontally Periodic Trapped Waves
214
Greens Functions
265
The NeumannKelvin Problem for a Submerged Body
318
TwoDimensional Problem for a SurfacePiercing Body
361
Existence and Properties
421
Bibliography
485
Name Index 505
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