On Stability of Linear Barbashin Type Integrodifferential Equations
Author
Source
Mathematical Problems in Engineering
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-5, 5 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-07-14
Country of Publication
Egypt
No. of Pages
5
Main Subjects
Abstract EN
We consider the Barbashin type equation ∂u(t,x)/∂t=c(t,x)u(t,x)+∫01k(t,x,s)u(t,s)ds+f(t,x) (t>0; 0≤x≤1), where c(·, ·), k(·, ·, ·), and f(·, ·) are given real functions and u(·, ·) is unknown.
Conditions for the boundedness of solutions of this equation are suggested.
In addition, a new stability test is established for the corresponding homogeneous equation.
These results improve the well-known ones in the case when the coefficients are differentiable in time.
Our approach is based on solution estimates for operator equations.
It can be considered as the extension of the freezing method for ordinary differential equations.
American Psychological Association (APA)
Gil', Michael. 2015. On Stability of Linear Barbashin Type Integrodifferential Equations. Mathematical Problems in Engineering،Vol. 2015, no. 2015, pp.1-5.
https://search.emarefa.net/detail/BIM-1075199
Modern Language Association (MLA)
Gil', Michael. On Stability of Linear Barbashin Type Integrodifferential Equations. Mathematical Problems in Engineering No. 2015 (2015), pp.1-5.
https://search.emarefa.net/detail/BIM-1075199
American Medical Association (AMA)
Gil', Michael. On Stability of Linear Barbashin Type Integrodifferential Equations. Mathematical Problems in Engineering. 2015. Vol. 2015, no. 2015, pp.1-5.
https://search.emarefa.net/detail/BIM-1075199
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1075199