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UDC 517.95

© Ya. T. Megraliev, 2012

ON SOLVABILITY OF AN INVERSE VALUE PROBLEM FOR PSEUDOHYPERBOLIC FOURTH ORDER EQUATION

In this paper an inverse problem for the pseudohyperbolic fourth order equation of with periodical boundary conditions is investigated. First of all the initial problem is reduced to the equivalent problem, for which the theorem of existence and uniqueness is proved. Then using these facts we prove the existence and uniqueness of the classical solution of the initial problem.

Keywords: inverse boundary problem, partial differential equation, Fourier’s method, classic solution.

References:

  1. Samarskiy A.A. O nekotorykh problemakh teorii differentsial`nykh uravneniy // Differentsial`nye uravneniya, 1980, t.16, ¹11, s.1925-1935.
  2. Cannon J. R. The solution of the heat equation subject to the specification of energy // Quart. Appl. Math., 1963, v.5, 21, p.155-160.
  3. Ionkin N.I. Reshenie odnoy kraevoy zadachi teorii teploprovodnosti s neklassicheskim kraevym usloviem // Differentsial`nye uravneniya, 1977, t.13, ¹2,  s.294-304.
  4. Nakhushev A.M. Ob odnom priblizhennom metode resheniya kraevykh zadach dlya differentsial`nykh uravneniy i ego priblizheniya k dinamike pochvennoy vlagi i gruntovykh vod // Differentsial`nye uravneniya, 1982, t.18,  ¹1, s.72-81.
  5. Budak B.M., Samarskiy A.A., Tikhov A.N. Sbornik zadach po matematicheskoy fizike. Moskva: Nauka, 1972, 668 s.
  6. Hudaverdiev K.I., Veliev A.A. Issledovanie odnomernoy smeshannoy zadachi dlya odnogo klassa psevdogiperbolicheskikh uravneniy tret`ego poryadka s nelineynoy operatornoy pravoy chast`yu, Baku: Chashyogly, 2010, 168 s.

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