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Articles

Weak Solutions of Boundary Value Problems in Nontube Domains for Fourth-Order Equations of Composite Type

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Pages 498-508 | Received 30 Aug 2010, Accepted 03 Jul 2011, Published online: 24 Aug 2011

References

  • Barozzi , G.C. 1960-1961 . Su alcuni problemi relative a une equazione lineare a dirivate parziali di tipo composito . Atti Semin. Mat. e Fis. Univ. Modena , 10 : 11
  • Yu M. Berezansky. Expansion in Eigenfunctions of Selfadjoint Operators . Naukova Dumka , Kiev , 1965 . in Russian
  • Burenkov V.I. Sobolev Spaces on Domains . B.G. Teubner, Stuttgart-Leipzig , 1998 .
  • Cattabriga , L. 1957 . Su alcuni problemi per equazioni differenziali di tipo composito . Rendiconti del Seminario Matematico della Universit di Padova , 27 : 122 – 143 .
  • Dainyak V.V. and Korzyuk V.I. Problem of Dirichlet type for linear differential equation of the third order . Differ. Uravn. , 23 5 : 867 - 872 , 1987 . in Russian
  • Davis R.B. A boundary value problem for third-order linear partial differential equations of composite type . Proc. Amer. Math. Soc. , 3 751 - 756 , 1952 . doi: Doi:10.1090/S0002-9939-1952-0050788-7 .
  • Davis R.B. A special case of the normal derivative problem for a third-order composite partial differential equation . Proc. Amer. Math. Soc. , 5 720 - 725 , 1954 . doi: Doi:10.1090/S0002-9939-1954-0064290-1 .
  • Dzhuraev T.D. On a certain boundary value problem for an equation of composite type . Dokl. Akad. Nauk Resp. Uzbekistan , 4 , 1962 . in Russian
  • Dzhuraev T.D. On a certain boundary value problem for equation . In Research on Differential Equations , pp. 46 - 51 , Tashkent , 1963 . in Russian
  • Eskin G.I. Boundary value problem for equation is elliptic operator . Siberian Math. J. , 3 6 : 882 - 911 , 1962 . in Russian
  • Eskin G.I. Boundary-value problems for equations with constant coefficients on the plane . Mat. Sb. , 59 101 : 67 - 104 , 1962 . in Russian
  • Hadamard , J. 1933 . Proprit'es d'une quation linaire aux drives partielles du quatrime ordre . Thoku Math. J. , 37 : 133 – 150 .
  • Hadamard , J. 1936 . Equations aux derivees partielles . L'enseignement mathematique , 35 : 5
  • Konopelko O.A. The boundary value problem for fourth-order equation of composite type . Vestn. BGU. Ser. , 1 3 : 73 - 79 , 2008 . in Russian
  • Konopelko O.A. Weak solutions of boundary value problems in tube domains for a fourth-order equation of composite type . Vestn. BGU. Ser. , 1 1 : 92 - 98 , 2010 . in Russian
  • Korzyuk V.I. Friedrichs' lemma for mollifiers with variable step . Vestn. BGU. Ser. , 1 2 : 55 - 71 , 1996 . in Russian
  • Korzyuk V.I. Equations of Mathematical Physics . BSU, Minsk , 2010 . in Russian
  • Korzyuk V.I. and Dainyak V.V. On weak solution of problem of Dirichlet type for linear differential equation of the third order . Differ. Uravn. , 28 6 : 1056 - 1066 , 1992 . in Russian
  • Korzyuk V.I. and Dainyak V.V. On solvability mixed problems for nonstationary equations of the third order . Vestn. BGU. Ser. , 1 3 : 54 - 60 , 2005 . in Russian
  • Korzyuk V.I. and Konopelko O.A. Weak solutions of boundary-value problems in tube domains for the fourth-order equation of composite type . Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series , 3 68 - 74 , 2009 . in Russian
  • Korzyuk V.I. and Konopel'ko O.A. Strong solution of boundary value problems in cylindrical domains for a fourth-order equation of composite type . Differ. Equ. , 46 5 : 690 - 701 , 2010 . doi: Doi:10.1134/S0012266110050083 .
  • Korzyuk V.I. , Konopel'ko O.A. and Cheb E.S. Boundary value problems for the fourth-order equations of hyperbolic and composite types . In Proceedings of the Fifth International Conference on Differential and Functional-Differential Equations (Moscow, August 17-24, 2008). Part 2, volume 36 of CMFD , pp. 87 - 111 , M., 2010 . PFUR. Available from Internet: http://mi.mathnet.ru/cmfd158 .
  • Mikhailov V.P. Partial Differential Equations . Nauka , Moscow , 1976 . in Russian
  • Sjstrand , O. 1936 . Sur une quation aux drives partielles du type composite . Arkiv Fr Matematik, Astronomi Och Fysik , 25A ( 21 ) : 1 – 11 .
  • Sjstrand , O. 1939 . Sur une quation aux drives partielles du type composite. Note 2 . Arkiv Fr Matematik, Astronomi Och Fysik , 26A ( 1 ) : 1 – 10 .

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