On stability of linear barbashin type integrodifferential equations
type: Item
instance of: scholarly article
title: On stability of linear barbashin type integrodifferential equations
zbMATH Open document ID: 1394.35536
DOI: 10.1155/2015/962565
published in: Mathematical Problems in Engineering
publication date: 2018-08-27T00:00:00Z
review text: Summary: We consider the Barbashin type equation \(\partial u(t, x) / \partial t = c(t, x) u(t, x) + \int_0^1 k(t, x, s) u(t, s) d s + f(t, x) (t > 0; 0 \leq x \leq 1)\), where \(c(\cdot, \cdot)\), \(k(\cdot, \cdot, \cdot)\), and \(f(\cdot, \cdot)\) are given real functions and \(u(\cdot, \cdot)\) 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.
Mathematics Subject Classification ID: 35R09
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 45K05
zbMATH DE Number: 6927702
Wikidata QID: Q59120071
author: Michael I. Gil'
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/962565
OpenAlex ID: W1607368079
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description: scientific article; zbMATH DE number 6927702