LEADER 04887nam 22006732 450 001 9910783045403321 005 20151005020621.0 010 $a1-107-12480-8 010 $a1-280-43047-8 010 $a9786610430475 010 $a0-511-17714-3 010 $a0-511-04196-9 010 $a0-511-15806-8 010 $a0-511-54677-7 010 $a0-511-32992-X 010 $a0-511-04469-0 035 $a(CKB)1000000000004695 035 $a(EBL)202412 035 $a(OCoLC)559554096 035 $a(SSID)ssj0000192632 035 $a(PQKBManifestationID)11183015 035 $a(PQKBTitleCode)TC0000192632 035 $a(PQKBWorkID)10197898 035 $a(PQKB)10945963 035 $a(UkCbUP)CR9780511546778 035 $a(Au-PeEL)EBL202412 035 $a(CaPaEBR)ebr10023548 035 $a(CaONFJC)MIL43047 035 $a(MiAaPQ)EBC202412 035 $a(PPN)261355007 035 $a(EXLCZ)991000000000004695 100 $a20090508d2002|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLinear water waves $ea mathematical approach /$fN. Kuznetsov, V. Maz?ya, B. Vainberg$b[electronic resource] 210 1$aCambridge :$cCambridge University Press,$d2002. 215 $a1 online resource (xvii, 513 pages) $cdigital, PDF file(s) 300 $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). 311 $a0-521-80853-7 320 $aIncludes bibliographical references and indexes. 327 $tIntroduction: Basic Theory of Surface Waves --$tMathematical Formulation --$tLinearized Unsteady Problem --$tLinear Time-Harmonic Waves (the Water-Wave Problem) --$tLinear Ship Waves on Calm Water (the Neumann-Kelvin Problem) --$tTime-Harmonic Waves --$tGreen's Functions --$tThree-Dimensional Problems of Point Sources --$tTwo-Dimensional and Ring Green's Functions --$tGreen's Representation of a Velocity Potential --$tSubmerged Obstacles --$tMethod of Integral Equations and Kochin's Theorem --$tConditions of Uniqueness for All Frequencies --$tUnique Solvability Theorems --$tSemisubmerged Bodies --$tIntegral Equations for Surface-Piercing Bodies --$tJohn's Theorem on the Unique Solvability and Other Related Theorems --$tTrapped Waves --$tUniqueness Theorems --$tHorizontally Periodic Trapped Waves --$tTwo Types of Trapped Modes --$tEdge Waves --$tTrapped Modes Above Submerged Obstacles --$tWaves in the Presence of Surface-Piercing Structures --$tVertical Cylinders in Channels --$tShip Waves on Calm Water --$tGreen's Functions --$tThree-Dimensional Problem of a Point Source in Deep Water --$tFar-Field Behavior of the Three-Dimensional Green's Function --$tTwo-Dimensional Problems of Line Sources --$tThe Neumann-Kelvin Problem for a Submerged Body --$tCylinder in Deep Water --$tCylinder in Shallow Water --$tWave Resistance --$tThree-Dimensional Body in Deep Water --$tTwo-Dimensional Problem for a Surface-Piercing Body --$tGeneral Linear Supplementary Conditions at the Bow and Stern Points --$tTotal Resistance to the Forward Motion --$tOther Supplementary Conditions. 330 $aThis 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, in turn, uses a plethora of mathematical techniques in the investigation of these three problems. Among the techniques used in the book the reader will find 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. For constructing examples of non-uniqueness usually referred to as 'trapped modes' the so-called inverse procedure is applied. Linear Water Waves will serve as an ideal reference for those working in fluid mechanics, applied mathematics, and engineering. 606 $aWave-motion, Theory of 606 $aWater waves$xMathematics 615 0$aWave-motion, Theory of. 615 0$aWater waves$xMathematics. 676 $a532/.593 700 $aKuznet?s?ov$b N. G$g(Nikolai? Germanovich),$01577656 702 $aMaz?i?a?$b V. G. 702 $aVai?nberg$b B. R$g(Boris Rufimovich), 801 0$bUkCbUP 801 1$bUkCbUP 906 $aBOOK 912 $a9910783045403321 996 $aLinear water waves$93856461 997 $aUNINA