On Well-posedness of Integro-differential Equations in Weighted L 2 ?spaces on Well-posedness of Integro-diierential Equations in Weighted L 2 -spaces
نویسندگان
چکیده
In this paper we consider the problem of constructing a well-posed state space model for a class of singular integro-diierential equations of neutral type. The work is motivated by the need to develop a framework for the analysis of numerical methods for designing control laws for aeroelastic and other uid/structure systems. Semigroup theory is used to establish existence and well-posedness results for initial data in weighted L 2 ?spaces. It is shown that these spaces lead naturally to the dissipativeness of the basic dynamic operator. The dissipativeness of the solution generator combined with the Hilbert space structure of these weighted spaces make this choice of a state space more suitable for use in the design of computational methods for control than previously used product spaces.
منابع مشابه
On Well - posedness of Integro - di erential Equations in WeightedL
In this paper we consider the problem of constructing a well-posed state space model for a class of singular integro-diierential equations of neutral type. The work is motivated by the need to develop a framework for the analysis of numerical methods for designing control laws for aeroelastic and other uid/structure systems. Semigroup theory is used to establish existence and well-posedness res...
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