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Original Articles

The Goursat problem for hyperbolic linear third order equations

Pages 270-279 | Received 08 Oct 2001, Published online: 14 Oct 2010

References

  • Hadamard , J. 1932 . Le probleme de Cauchy Paris
  • Hadamard , J. 1933 . Proprietes d'une equation linaire aux derivees partielles du quatrieme order . Tohuku Math. J. , 37 : 133 – 150 .
  • Hadamard , J. 1936 . Equations aux derivees partielles . L'enseignement mathematique , 35 : 5 – 42 .
  • Petrovsky , I.G. 1937 . Über das Cauchysche Problem für Systeme von partieller Differentialqle‐ichungen . Matematichesky sbornik , 2 (44) : 815 – 870 .
  • Petrovsky , I.G. 1939 . Sür l'analyticite des solutions des systemes d'equations differentielles . Matematichesky sbornik , 5 (47) : 3 – 70 .
  • Garding , L. 1958 . Solution directe au probleme de Cauchy pour les equations hyperboliques , Paris : C.N.R.S. . (in French)
  • Garding , L. 1957 . Cauchy's problem for hyperbolic equations , Winter and Spring Quarters. University of Chicago .
  • Kreiss , H.O. 1969 . Initial ‐ boundary value problems for hyperbolic systems . Comm/ Pure Appl. Math. , 23 : 277 – 298 .
  • Sakamoto , R. 1970 . Mixed Problems for hyperbolic equations . Math. Kyoto Univ. , 10 : 349 – 373 . 403 – 417 .
  • Leray , J. 1952 . Lectures on Hyperbolic equations with variable coefficients . Priston, Just for Adv. Study ,
  • Leray , J. 1955 . Hyperbolic differential equations , New York : The Institute for Advaced Study .
  • Lions , J.‐L. 1969 . Quelques methodes de resolution des problemes aux limites non lineaires Paris
  • Grinberg , G.A. 1967 . About one possible method of approach to problems of heat conductivity, diffusion, wave process, and similar in the presence of moving boundaries and about some other applications of the method . Prikladnaya matematica i informatika , 31 (2) : 193 – 203 . (in Russian)
  • Dragieva , N.A. 1975 . Application of Galerkin's method to solution of wave equation in domain with moving boundaries . Journal vychislitelnoj matematiki i matematicheskaya fizika , 15 (4) : 946 – 956 . (in Russian)
  • Eskin , G. 1962 . Boundary problems for equations with constant coefficients on two ‐ dimensional subspace . Matematicheski sbornik , 59 (101) : 67 – 104 . (in Russian)
  • Eskin , G. 1962 . General boundary problems for equations of the main type with two independent variables . Matematicheski sbornik , 59 (101) : 105 – 124 . (in Russian)
  • Eskin , G. 1962 . Boundary problem for equation elliptic operator . Sibirski matematicheski zhurnal , 3 (6) : 882 – 911 . (in Russian)
  • Thomee , V. 1955 . Estimates of the Friedrichs ‐ Lewy type for a hyperbolic equation with three characteristics . Math. Scand. , 3 : 115 – 123 .
  • Thomee , V. 1957 . Estimates of the Friedrichs ‐ Lewy type for mixed problems in the theory of linear hyperbolic differential equation in two independent variables . Math. Scand. , 5 : 93 – 113 .
  • Thomee , V. 1958 . Existence proofs for mixed problems for hyperbolic differential equations in two independent variables by means of the continuity method . Math. Scand. , 6 : 5 – 32 .
  • Korzyuk , V.I. 1996 . The method of energy inequalities and mollifying operators . Vestnik Bel‐gosuniversiteta. Ser.1. Fizika, Matematika, Informatika , 3 : 55 – 71 . (in Russian)
  • Burenkov , V.I. 1998 . Sobolev spaces on domains , Stuttgart, Leeipziq : Teubner .
  • Samarski , A.A. , Vabishchevich , P.N. , Lemeshevsky , S.V. and Matus , P.P. 1998 . Difference schemes for conjugation problem of hyperbolic and parabolic equations . Sib. Matem. Zhurnal , 39 (4) : 954 – 962 . (in Russian)
  • Korzyuk , V.I. 1998 . Problems for Nostationary Polytypic Equations with Conditions of Conjugations . Second International Conference “Finite ‐ Difference Methods: Theory and Application “ , 2 : 75 – 79 .
  • Korzyuk , V.I. , Lemeshevsky , S.V. and Matus , P.P. 1999 . Conjugation problem about jointly separate flow of viscoelastic and viscous fluids in the plane duct . Mathematical Modelling and Analysis , 4 : 114 – 123 .
  • Korzyuk , V.I. and Lemeshevsky , S.V. 2001 . Problems on conjugation of polytypic equations . Mathematical Modelling and Analysis , 6 (1) : 106 – 116 .
  • Korzyuk , V.I. 1968 . The problem about conjugation of equations of hyperbolic and parabolic types . Differ. Uravnenia , 4 (10) : 1855 – 1866 . (in Russian)
  • Dezin , A.A. 1980 . General Topics of the Theory of Boundary Problems , Moscow : Nauka . (in Russian)
  • Korzyuk , V.I. 1970 . Mixed problem for some nonstationary equations with discontinuous coefficients . Differ. Uravnenia , 6 (2) : 343 – 357 . (in Russian)

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