On an infinite-dimensional differential equation in vector distribution with discontinuous regular functions in a right hand side. (1996)

• Record Type: Journal Article
• Authors: Basin, Michael V.
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 9:Number 1(1996)
• Page Start: 1
• Page End: 10
• Publication Date: 1996
• Subjects: infinite-dimensional equation -- discontinuous right-hand side -- distribution; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953396000019
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : An infinite-dimensional differential equation in vector distribution in a Hilbert space is studied in case of an unbounded operator and discontinuous regular functions in a right-hand side. A unique solution ( vibrosolution ) is defined for such an equation, and the necessary and sufficient existence conditions for a vibrosolution are proved. An equivalent equation with a measure, which enables us to directly compute jumps of a vibrosolution at discontinuity points of a distribution function, is also obtained. The application of the obtained results to control theory is discussed in the conclusion.