East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
권호 표지
DOI QR코드

DOI QR Code

ON AN EQUATION CONNECTED WITH THE THEORY FOR SPREADING OF ACOUSTIC WAVE

  • Zikirov, O.S. (Faculty of Mechanics and Mathematics National University of Uzbekistan)
  • Received : 2010.06.14
  • Accepted : 2011.01.03
  • Published : 2011.01.31
Download PDF
⟨ Previous Next ⟩

Abstract

In the paper, we study questions on classical solvability of nonlocal problems for a third-order linear hyperbolic equation in a rectangular domain. The Riemann method is applied to the Goursat problem and solution is obtained in the integral form. Investigated problems are reduced to the uniquely solvable Volterra-type equation of second kind. Influence effects of coefficients at lowest derivatives on correctness of studied problems are detected.

Keywords

References

  1. G. N. Barenblatt, Yu. P. Jeltov and I. N. Kochina, Basic consepts in the theory of seepage of homogeneous liquids in bissured rocks, J. Appl. Math. Mech. 24(5) (1960), 1286-1303. https://doi.org/10.1016/0021-8928(60)90107-6
  2. A. V. Bitsadze, Some classes of partial differential equations, Nauka, Moscow, 1981(in Russian).
  3. A. Bouziani, On the solvability of a nonlocal problem arising in dynamics of moisture transfer, Georgian Mathematical Journal 10(4) (2003), 607-627.
  4. A. Bouziani and M. S. Temsi, On a Quasilinear Pseudohyperbolic Equations with a nonlocal Boundary Conditions, Internat. J. Math. Analysis 3(3) (2009), 109-120.
  5. E. S. Dzektser, Equation of the motion of underground waters with free surface in multilayer medis, Dokl. Akad. Nauk SSSR 220(3), 540-543, (1975)(in Russian).
  6. O. M. Dzhokhadze, A General Darboux-Type Boundary Value Problem in Curvilinear Domains with Corners for a Third-Order Equation with Dominated Lower-Order Terms, Sibirian Mathematical Journal 43(2) (2002), 235-250. https://doi.org/10.1023/A:1014745121563
  7. T. D. Dzhuraev, Boundary-value problems for the mixed and mixed-composite type equations, Fan, Tashkent, 1979(in Russian).
  8. T. D. Dzhuraev and O. S. Zikirov, The Goursat problem and a non-local problem for a class of third-order equations, In Non-classical equations of mathematical Physics, pp. 98-109, Novosibirsk, 2005. Institute of Mathematics (in Russian).
  9. V. I. Jegalov and A. N. Mironov, Differential Equations with older partial derivatives, Kazan, 2001(in Russian).
  10. A. I. Kozhanov, On a nonlocal boundary value problem with variable coefficients for the heat equation and the Aller equation, Diffensialniye uravneniya 40(6), 763-774, 2004(in Russian).
  11. A. M. Nakhushev, Problems with Displacements for Partial Differential Equations, Nauka, Moscow, 2006(in Russian).
  12. A. M. Nakhushev, Equations of Mathematical Biology, Vysshaya shkola, Moscow, 1995(in Russian).
  13. Kh. A. Rakhmatulin and Yu. A. Dem'yanov, Strength at intense short-time loading, Logos, Moscow, 2009(in Russian).
  14. O. V. Rudenko and S. N. Soluyan, Technical Bases of the Non-linear Acoustics, Nauka, Moscow, 1975(in Russian).
  15. M. Sapagovas, On the stubility of a finite-difference scheme for nonlocal parabolic equations boundary-value problem, Lietuvos Matematikos Rinkinys 48(3) (2008), 339-356.
  16. M. Kh. Shkhanukov, On some boundary value problems for a third-order equation arising when modeling fluid filtration in porous media, Differensialniye uravneniya 18(4), 689-699, 1982(in Russian).
  17. A. Stikonas A and O. Stikoniene, Characteristic functions for Sturm-Lioville problems with nonlocal boundary-value problem, Mathemtical Modelling and Analysis 14(2) (2009), 229-246. https://doi.org/10.3846/1392-6292.2009.14.229-246
  18. V. V. Varlamov, Time estimates for the Cauchy problem for a third-order hyperbolic equation, Internat. J. Math. and Math. Sci. 33(17) (2003), 1073-1981.
  19. O. S. Zikirov, On boundary-value problem for hyperbolic-type equation of the third order, Lietuvos Matematikos Rinkinys 47(4) (2007), 591-603.
  20. O. S. Zikirov, A non-local Boundary Value Problems for Third-Order Linear Partial Differential Equation of Composite Type, Mathemtical Modelling and Analysis 14(3) (2009), 407-421. https://doi.org/10.3846/1392-6292.2009.14.407-421