Email this article 
PROBLEM WITH TIME-DEPENDENT BOUNDARY CONDITIONS FOR HYPERBOLIC EQUATION
- Authors: Dyuzheva A.V.1
-
Affiliations:
- Samara National Research University
- Issue: Vol 23, No 1 (2017)
- Pages: 7-14
- Section: Articles
- URL: https://journals.ssau.ru/est/article/view/5141
- DOI: https://doi.org/10.18287/2541-7525-2017-23-1-7-14
- ID: 5141
Cite item
Full Text
Abstract
In this paper, we consider a problem for hyperbolic equation with standard initial data and nonlocal dynamic conditions. Such conditions may arise when a thick short bar fixed by point forces and springs. The existence and uniqueness of the problem are proved. The proof is mainly based on a priori estimates and Galerkin procedure.
About the authors
A. V. Dyuzheva
Samara National Research University
Author for correspondence.
Email: morenov@ssau.ru
Russian Federation
References
- Gording L. Zadacha Koshi dlia giperbolicheskikh uravnenii . M.: Iz-vo inostrannoi literatury, 1961, 120 p. .
- Kozhanov A.I. Nelokal’nye zadachi dlia lineinykh giperbolicheskikh uravnenii s granichnymi usloviiami, soderzhashchimi vremennuiu proizvodnuiu . In: Doklady AMAN, 2010, Vol. 12, no. 1б, pp. 40–52 .
- Ladyzhenskaya O.A. Kraevye zadachi matematicheskoi fiziki . M.: Nauka, 1973, 407 p. .
- Lazhetych N.L. O klassicheskoi razreshimosti smeshannoi zadachi dlia odnomernogo giperbolicheskogo uravneniia vtorogo poriadka . Differents. uravneniia , 2006, Vol. 42, No. 8, pp. 1072–1077 .
- Pulkina L.S., Dyuzheva A.V. Nelokal’naia zadacha s peremennymi po vremeni kraevymi usloviiami Steklova dlia giperbolicheskogo uravneniia . , 2010, no. 4(86), pp. 56–64 .
- Steklov V.A. Osnovnye zadachi matematicheskoi fiziki . M.: Nauka, 1983 .
- Tikhonov A.N., Samarskii A.A. Uravneniia matematicheskoi fiziki . M.: Nauka, 1977 .
Supplementary files
