A. I. Dvirnyj, V. I. Slyn'ko, “Stability in terms of two measures for a class of semilinear impulsive parabolic equations”, Mat. Sb., 2013, Volume 204, Number 4,Pages <nobr>25

This article is cited in 3 papers

Stability in terms of two measures for a class of semilinear impulsive parabolic equations

A. I. Dvirnyj^a, V. I. Slyn'ko^b

^a Hedmark University College
^b Institute of Mechanics named after S. P. Timoshenko of National Academy of Sciences of Ukraine

Abstract: The problem of stability in terms of two measures is considered for semilinear impulsive parabolic equations. A new version of the comparison method is proposed, and sufficient conditions for stability in terms of two measures are obtained on this basis. An example of a hybrid impulsive system formed by a system of ordinary differential equations coupled with a partial differential equation of parabolic type is given. The efficiency of the described approaches is demonstrated.
Bibliography: 24 titles.

Keywords: stability in a cone, impulsive effect, semilinear parabolic equation, semiordering, comparison principle.

UDC: 517.925.51+517.956.4

MSC: 34A37, 34D40

Received: 29.11.2011 and 06.07.2012

DOI: 10.4213/sm8091