Publication Cover
Applicable Analysis
An International Journal
Volume 54, 1994 - Issue 3-4
16
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

A Function-theoretic approach to a two-dimensional transient wave-body interaction problem

&
Pages 283-303 | Published online: 02 May 2007

References

  • Abraowitz , M. and Stegun , I. 1970 . Handbook of mathematical functions , New York : Dover Publ. Inc. .
  • Adachi , H. and Ohmatsu , S. 1980 . “ On the time-dependent potential and its application to wave problems ” . In In Pro. 13th Symposium on Naval Hydrodynamics , 281 – 302 . Washington, DC : Office of Naval Research .
  • Athanassoulis , G. A. 1984 . An expansion theorem for water wave potentials . J. Engrg. Math. , 18 : 181 – 194 .
  • Athanassoulis , G. A. 1987 . On the solvability of a two-dimensional water-wave problem . Quart. Appl. Math. , XLIV ( 4 ) : 601 – 620 .
  • Athanassoulis , G. A. and Makrakis , G. N. 1989 . Causality and radiation condition in free-surface hydrodynamics , Athens, , Greece : In Proc. Second National Congress on Mechanies .
  • Beale , J. T. 1977 . Eigenfunction expansions for objects floating in an open sea . Comm. Pure Appl. Math. , XXX : 283 – 313 .
  • Beck , R. F. and Liapis , S. 1987 . Transient motions of floating bodies at zero forward speed . J. Ship Res. , 31 ( 3 ) : 164 – 176 .
  • Cartan , H. 1963 . Elementary theory of analytic functions of one or several complex variables , Paris : Editions Scientifiques Hermann .
  • Dobrokhotov , S. Y. and Zevandrov , P. N. 1968 . Nonstandard characteristics and maslov's operatorial method in linear problems concerning unsteady water waves . Anal. Appl. , : 285 – 295 .
  • Doetch , G. 1974 . Introduction to the theory and application of the Laplace trans-formation , New York : Springer-Verlag .
  • Erdelyi , A. 1953 . Higher transcendental functions , New York : mcGraw-Hill Book Co .
  • Finkelstein A.B. The initial value problem for transient water waves Dissertation PhD thesis University New York 1953
  • Finkelstein , A. B. 1957 . The initial value problem for transient waves . Comm. Pure Appl. Math. , 10 : 511 – 522 .
  • Friedman , A. and Shinbrot , M. 1967 . The initial value problem for the linearized equations of water waves . J. Math. Mech. , 17 ( 2 ) : 107 – 196 .
  • Garipov , R. M. 1967 . Asymptotics of cauchy-poisson waves . Amer. Math. Soc. Translation , 104 ( 2 ) : 119 – 128 .
  • Garipov , R. M. 1967 . On the linear theory of gravity waves: the theorem of exoistence and uniqueness . Arch. Rational Mech. Appl. , 24 ( 2 ) : 352 – 362 .
  • Gradshteyn , I. S. and Ryzhik , I. M. 1965 . Table of integrals series and products , New York : Academic Press .
  • Grue , J. and Palm , E. 1985 . Wave rediation and wave differaction from a submerged body in a uniform current . J. Fluid Mech. , 151 : 257 – 278 .
  • Jones , D. S. 1966 . Generalized functions , London : mcGraw-Hill Publ. Co. .
  • Kalla , S. L. and Ross , B. 1985 . “ The development of functional relations by means of fractional operators, in fractional calculus ” . In In A. Mc. Bride and G.F. Roach , Pitman .
  • Kossioris , G. T. and Athanassoulis , G. A. 1988 . Series expansions of solutions of plane elliptic partial differential equations in domains of arbitrary shape . Applicable Analysis , 27 : 253 – 269 .
  • Lamb , H. 1945 . Hydrodynaics , New York : Dover Publ. Inc .
  • Lau , B. R. 1972 . The linearized equations of water waves . Indiana Univ. Math. J. , 22 ( 2 ) : 233 – 266 .
  • Licht , C. 1982 . Evolution d'um sustem fluide-flotteur . J. Mec. Theor. Appl. , 1 ( 2 ) : 211 – 235 .
  • Maskell , S. J. and ursell , F. 1970 . The transient motion of a floating body . J. Fluid Mech. , 44 ( 2 ) : 303 – 313 .
  • Mei , C. C. 1982 . The Applied Dynamics of Ocean Surface Waves , New York : John Wiley and Sons .
  • Naimark , M. A. 1972 . Normed algebras . Wolters-Noordhoff Publishing Groningen The netherlands ,
  • Newman , J. N. 1985 . Transient axisymmetric motion of folating cylinders . J. Fluid Mech. , 157 : 17 – 33 .
  • Niremberg , L. 1972 . An Abstract form of the nonlinear cauchy-kowalewski theore . J. Differential Geom. , 6 : 561 – 576 .
  • Nishida , T. 1977 . A note on nireberg's theorem as an abstract form of the non-linear cauchy-kowalewski theore in a scale of banach spaces . J. Differntial Geom. , 12 : 629 – 633 .
  • Sansone , G. and Gerretsen , J. 1960 . lectures on the theory of functions of a complex variable. I. holoorphic functions . Noordhoff International Publ., leyden , 12
  • Sedov , L. I. 1969 . Similarity and dimensional methods in mechanics , New York : Academic Press .
  • Sith , C. M. 1982 . The transient motion of a partially immersed rolling strip in water . IMA J. Appl. Math. , 29 : 59 – 77 .
  • Stoker , J. J. 1957 . Water waves , New York : Interscience Publi. Inc .
  • Treves , F. 1975 . Basic linear partial differential equaions , New York : Academic Press .
  • Tutschke , W. 1989 . Solution of initial value problems in classes of generalized analytic functions , Heidelberg : Springer Verlag .
  • Ursell , F. 1964 . The decay of the free motion of a floating body . J. Fluid Mech. , 105 : 305 – 319 .
  • Vladimirov , V. S. 1979 . Generalized functions in mathematical physics , Moscow : Mir Publ .
  • Walter , W. 1985 . An elementary proof of the Cauchy-Kowalewski theorem . Amer. Math. Monthly , 92 : 115 – 125 .
  • Weber C.F The Existence and Decay of Water Waves in the Presence of a Fixed Obstacle PhD thesis New York 1976
  • Wehausen , J. V. and Laiton , E. V. 1960 . “ Surface Waves, of Fluid Dynamics III ” . In Encycl. of Physics , Springer-Verlag .
  • Widder , D. V. 1975 . The heat equation , New York : Academic Press .
  • Yeung , R. W. 1982 . The transient heaving motion of floating chlinders . J. Engrg. Math. , 16 : 97 – 119 .
  • Zami , A. 1981 . “ Numerical solving of transient linear hydrodynaics problems by coupling finite elements and integral representation ” . In In Proc. Third International Conference on Numerical Ship Hydrodynamics Paris
  • Zeminian , A. H. 1965 . Distributin Theory and Transform Analysis , New York : McGraw-Hill Book Co .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.