[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.7858/eamj.2011.27.1.051

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

Zikirov, O.S. (Faculty of Mechanics and Mathematics National University of Uzbekistan)

Publication Information

East Asian mathematical journal / v.27, no.1, 2011 , pp. 51-65 More about this Journal

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

Third-order equation; wave operator; conditions; nonlocal problem; the Goursat problem; the Riemann function; integral equation; solvability;

Citations & Related Records

Reference

1	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. DOI
2	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.
3	O. S. Zikirov, On boundary-value problem for hyperbolic-type equation of the third order, Lietuvos Matematikos Rinkinys 47(4) (2007), 591-603.
4	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. DOI
5	V. I. Jegalov and A. N. Mironov, Differential Equations with older partial derivatives, Kazan, 2001(in Russian).
6	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).
7	A. M. Nakhushev, Problems with Displacements for Partial Differential Equations, Nauka, Moscow, 2006(in Russian).
8	A. M. Nakhushev, Equations of Mathematical Biology, Vysshaya shkola, Moscow, 1995(in Russian).
9	Kh. A. Rakhmatulin and Yu. A. Dem'yanov, Strength at intense short-time loading, Logos, Moscow, 2009(in Russian).
10	O. V. Rudenko and S. N. Soluyan, Technical Bases of the Non-linear Acoustics, Nauka, Moscow, 1975(in Russian).
11	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.
12	A. Bouziani, On the solvability of a nonlocal problem arising in dynamics of moisture transfer, Georgian Mathematical Journal 10(4) (2003), 607-627.
13	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).
14	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. DOI ScienceOn
15	A. V. Bitsadze, Some classes of partial differential equations, Nauka, Moscow, 1981(in Russian).
16	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.
17	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).
18	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. DOI ScienceOn
19	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).
20	T. D. Dzhuraev, Boundary-value problems for the mixed and mixed-composite type equations, Fan, Tashkent, 1979(in Russian).