ABOUT ONE TASK WITH A NONLOCAL CONDITION ON TIME VARIABLE FOR THE HYPERBOLIC EQUATION


Cite item

Abstract

In this article, boundary value problem for hyperbolic equation with nonlocal initial data in integral form is considered. The main result is that the nonlocal problem is equivalent to the classical boundary value problem for a loaded equation. This fact helps to prove the uniqueness of a solution to the problem.

About the authors

S. V. Kirichenko

Samara State University of Railway Transport

Author for correspondence.
Email: morenov@ssau.ru

References

  1. Cannon J.R. The solution of the heat equation subject to the specification of energy. Quart. Appl. Math., 1963, no. 21, pp. 155–160 .
  2. Gushchin A.K., Mihailov V.P. O razreshimosti nelokalnykh zadach dlya ellipticheskogo uravneniya vtorogo poryadka . Matem. sb. , 1995, 81:1, pp. 101–136. DOI: http://dx.doi.org/10.1070/SM1995v081n01ABEH003617 .
  3. Skubachevsky A.L. Neklassicheskie kraevye zadachi. I . Sovremennaya matematika. Fundamentalnye napravleniya , 2008, 155:2, pp. 199–334. DOI: https://doi.org/10.1007/s10958-008-9218-9 .
  4. Gordeziani D.G., Avalishvili G.A. Resheniya nelokal’nykh zadach dlya odnomernykh kolebanii sredy . Matem. modelir. , 2000, Vol. 12, no. 1, pp. 94–103. Available at: http://mi.mathnet.ru/mm832 .
  5. Kozhanov A.I., Pulkina L.S. O razreshimosti kraevykh zadach s nelokal’nym granichnym usloviem integral’nogo vida dlya mnogomernykh giperbolicheskikh uravnenii . Differents. Uravneniia , 2006, Vol. 42, no. 9, pp. 1233–1246. DOI: https://doi.org/10.1134/S0012266106090023 .
  6. Pulkina L.S. Kraevye zadachi dlya giperbolicheskogo uravneniya s nelokalnymi usloviyami 1 i 2-go roda . Izvestiya vuzov. Matematika , 2012, Vol. 56, no. 4, pp. 74–83. Available at: https://kpfu.ru/portal/docs/F19962257/08_04ref.pdf .
  7. Samarskii А.А. O nekotorykh problemakh sovremennoi teorii differentsial’nykh uravnenii . Differents. uravneniia , 1980, Vol. 16, no. 11, pp. 1925–1935. Available at: http://mi.mathnet.ru/de4116 .
  8. Zdenek P. Bazant, Milan Jirasek. Nonlocal Integral Formulation of Plasticity And Damage: Survey of Progress. American Society of Civil Engineers. Journal of Engineering Mechanics, 2002, pp. 1119–1149. DOI: https://doi.org/10.1061/(ASCE)0733-9399(2002)128:11(1119) .
  9. Ladyzhenskaya O.А. Kraevye zadachi matematicheskoi fiziki . М.: Nauka, 1973, 407 p. Available at: https://mexalib.com/view/25085 .

Copyright (c) 2019 С. В. Кириченко

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies