Abstract
We consider four mixed problems for the string vibration equation with homogeneous boundary and inhomogeneous nonlocal conditions of the first or second kind and with zero initial conditions. By using recursion relations, we find generalized solutions of the abovementioned problems.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Il’in, V.A., Boundary Control of Vibrations on Two Ends in Terms of the Generalized Solution of the Wave Equation with Finite Energy, Differ. Uravn., 2000, vol. 36, no. 11, pp. 1513–1528.
Kholomeeva, A.A., Optimization of a Nonlocal Boundary Control of the Vibrations of a String with a Fixed End for an Arbitrary Time Interval That Is a Multiple of 2l, Differ. Uravn., 2008, vol. 44, no. 5, pp. 696–700.
Il’in, V.A., Uniqueness of Generalized Solutions of Mixed Problems for the Wave Equation with Nonlocal Boundary Conditions, Differ. Uravn., 2008, vol. 44, no. 5, pp. 672–680.
Author information
Authors and Affiliations
Additional information
Original Russian Text © A.A. Kuleshov, 2010, published in Differentsial’nye Uravneniya, 2010, Vol. 46, No. 1, pp. 98–104.
Rights and permissions
About this article
Cite this article
Kuleshov, A.A. Mixed problems for the string vibration equation with homogeneous boundary conditions and inhomogeneous nonlocal conditions. Diff Equat 46, 101–107 (2010). https://doi.org/10.1134/S0012266110010106
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0012266110010106