THE EXISTENCE OF A SOLUTION OF A NONLOCAL PROBLEM FOR THE WAVE EQUATION OF A STRING
Keywords:
inverse problem, wave equation of string, nonlocal problem, Fourier method, boundary conditions.Abstract
The wave equation of string is a fundamental model that describes the behavior of oscillating systems, and the nonlocal problem is a type of boundary value problem that arises in various physical contexts. In this article, a comprehensive overview of the existence of a solution to a nonlocal problem for the wave equation of string is provided and an inverse problem is used to solve it. As a result, the problem is reduced to a classical problem, namely the first mixed problem for the wave equation of a string, and it is solved using the Fourier method.
References
Tikhonov A.N., Samarsky A.A. Equations of Mathematical Physics. –M.: Nauka, 1966. – 736 p.
Salokhiddinov M.S. Equations of Mathematical Physics. - T.: Uzbekistan, 2002. 44-61 p.
Beylin S.A. Nonlocal Problem with Integral Condition for One-Dimensional Wave Equation // Proc. XXIV Conf. of Young Scientists of the Mech.-Math. Faculty of Lomonosov Moscow State University, Vol. I. – 2002. - 24-26 p.
Beylina N.V. On a Nonlocal Problem for the String Oscillation Equation, Math. Modeling and Boundary Problems, 2007, part 3, 32–35 p.
Zikirov O.S. Equations of Mathematical Physics. – T.: Fan va texnologiya, 2017. –16-23 p.
Sobolev S.L. Equations of Mathematical Physics. –M.: Nauka, 1966. – 28-32 p.
Salokhiddinov M.S., Islomov B.I. Collection of Problems in Equations of Mathematical Physics. – T.: Mumtoz so’z, 2010. – 41-68 p.
Vladimirov V.S. Equations of Mathematical Physics. –M.: Nauka, 1981.–38-42 p.
Koshlyakov N.S., Gliner E.B., Smirnov M.M. Equations in Partial Derivatives of Mathematical Physics. – M.: Higher School, 1970. – 54-61 p., 75-83 p.
Joraev T.J., Abdinazarov S. Equations of Mathematical Physics. Tashkent. 2003. 332 p.
Bitsadze A.V. Equations of Mathematical Physics. Moscow. 1976. 296 p.
Mikhlina S.G. Course of Mathematical Physics. Lan. 2002. 576 p.
Zikirov O.S. Partial Differential Equations. Tashkent. “University” 2012. 260 p.
Smirnov M.M. Collection of Problems in Equations of Mathematical Physics. Moscow. 2004. 798 p.
Sabitov K.B. Equations of Mathematical Physics. 2013. 352 p
