On existence and uniqueness of solutions of a class of perturbed second order evolution equations

In this paper, properties of operators of the kind A + Λ are investigated, where A is a selfadjoint, positive definite differential operator with compact inverse on a Hilbert space, and Λ is assumed to be A-bounded, A-symmetric and A-positive semidefinite. A general theory on the existence and uniqu...

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Bibliographic Details
Published inSystems & control letters Vol. 17; no. 5; pp. 401 - 408
Main Author Luo, Zheng-Hua
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 1991
Elsevier
Subjects
Applied sciences
Computer science; control theory; systems
Control theory. Systems
Exact sciences and technology
Existence and uniqueness of solutions
perturbed second order evolution equation
System theory
Existence and uniqueness of solutions
perturbed second order evolution equation
Operator
Solution uniqueness
Second order equation
Existence theorem
Flexible structure
Eigenvalue
Evolution equation
Hilbert space
Perturbation
Dynamic model
Beam(mechanics)
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Summary:In this paper, properties of operators of the kind A + Λ are investigated, where A is a selfadjoint, positive definite differential operator with compact inverse on a Hilbert space, and Λ is assumed to be A-bounded, A-symmetric and A-positive semidefinite. A general theory on the existence and uniqueness of solutions of second order evolution equations involving the operator A + Λ is developed. The new findings obtained in this paper have potential applications in modeling and control of flexible structures.
ISSN:0167-6911
1872-7956
DOI:10.1016/0167-6911(91)90140-A