D. L. Russell, Controllability and stabilizability theory for linear partial dierential equations: recent papers and open questions, SIAM Review 20 (1978), pp. 639-739.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Markus. Based on the implicit function theorem, Markus [17] studied the local controllability problem for nonlinear finite dimensional ordinary di#erential equations. Subsequently, the implicit function type method was applied to nonlinear wave equations by Fattorini [5] Chewning [3] and Russell [19] and nonlinear plate equations [16] More recently, Lagnese [9] developed a method of contraction mapping principle type to prove local controllability for nonlinear partial di#erential equations governing the evolution of the von Karman plate. On the other hand, using Schauder s fixed point ....

D.L. Russell, Controllability and stabilizability theory for linear partial di#erential equations: recent progress and open questions, SIAM Rev. 20 (1978), 639-739.

....fl ) 0 j 1 : Given the representation (27) for the solution [ t ; proving the asserted exact controllability at given time T 0 (Theorem 1. 1) is then equivalent to the functional analytical principle of showing the surjectivity of the operator L T , where L T is defined in (25) see [19] and [21] Note that L T is well defined as an element of L i [L 2 (0; T ; L 2 ( Omega Gamma84 2 ; Theta D Gamma A fl Delta 0 j , as B is (see Remark 2.4 below) therefore, the control operator L T as a mapping into the state space H fl makes sense a priori only as an ....

D. Russell, Controllability and stabilizability theory for linear partial differential equations: recent progress and open questions, SIAM Review, vol. 20, No. 4 (1978), 639--739.

....space E. 3 Abstract Formulation of the System (1.1) In order to prove the main result, we will use a technique developed first by Lee and Markus (see [10] for systems of ordinary differential equations. This technique has since been adapted for infinite dimensional systems. See, for example, [5, 12, 6]. We note that the results in [6] correspond to global controllability results. This work is also quite beneficial for the current problem, with modifications on the assumptions) To employ this technique, we first must put the system (1.1) into an abstract o.d.e. framework over the Hilbert spaces ....

D. L. Russell. Controllability and stabilizability theory for linear partial differential equations: Recent progress and open questions, SIAM Review, 20:4 (1978), 639 - 739.

.... all initial data in D Theta D are exactly L 2 controllable in fl at time T (see [5] for the definition of the Beurling Malliavin density and [13] for the applications to control theory) This implies that, in the same case, we cannot obtain uniform stabilization in the energy space (cf. 18] [21]) Let us also notice that the lack of exact controllability in the usual Sobolev spaces for the Kirchhoff model also follows from a result proved in [22] 5. An example Suppose that Omega is a rectangle of the form (0; Theta (0; L) In order to do some explicit computations we assume that ....

D. L. Russell, Controllability and stabilizability theory for linear partial differential equations, SIAM Review, 20(1978), 639-679.

....stabilization problem was studied in [7] 14] The main results obtained in these papers assert that we have strong stabilization for a dense set of control points, called strategic . In the same one dimensional case, by the use of Russell s stabilizability controllability arguement (see [21]) we can see that the energy decay is not exponential (see [12] 14] We shall generalize the results obtained in the one dimensional case by proving the existence of a dense set of strategic curves such that every solution of ( 1.1) 1.3) decays to zero when t tends to infinity and that ....

D. L. Russell, Controllability and stabilizability theory for linear partial differential equations, SIAM Review, 20(1978), 639-679.

.... action, due to the absence of direct and inverse inequalities involving the same Sobolev spaces; cf. e.g. 32] 3) There are many former results where estimates of this type were obtained for general domains with particular choices of the operators P and Q; see, e.g. 6] 16] 24] 35] [36], 39] 40] However, in these results we never had # 1 (2R) where R denotes the radius of the smallest ball containing## (Estimates with # = 1 (2R) were obtained in [16] The fact that arbitrarily large decay rates can be achieved by boundary feedbacks of this type seems to be new. Let us ....

D. L. RUSSELL, Controllability and stabilizability theory for linear partial di#erential equations. Recent progress and open questions, SIAM Rev., 20 (1978), pp. 639--739.

....controllability. We replace stabilizabilty by the less restrictive requirement of optimizability. As a corollary to our main result, we show that if A generates a strongly continuous bounded group and (A; B) is optimizable, then (A; B) is controllable. 1. Introduction and Preliminaries In Russell [5], Section 5, exact controllability for a wave equation with boundary control was established by showing that the system was both stabilizable and backwards stabilizable. This approach was a generalization of a finite dimensional result given in Russell [4] and has been subsequently used to prove ....

D.L. Russell, "Controllability and stabilizability theory for linear partial differential equations - recent progress and open questions", SIAM Review 20, pp. 639--739, (1978).

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D. L. Russell, Controllability and stabilizability theory for linear partial dierential equations: recent papers and open questions, SIAM Review 20 (1978), pp. 639-739.

No context found.

D.L. Russell, Controllability and stabilizability theory for linear partial di#erential equations, recent progress and open questions, SIAM REVIEW 20 (1978), 639--739.

No context found.

D. L. Russell, Controllability and stabilizability theory for linear partial di#erential equations: recent progress and open questions, SIAM Rev., 20 (1978), 639-739.

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D.L. Russell, Controllability and stabilizability theory for linear partial di#erential equations: recent progress and open questions, SIAM Rev., 20 (1978), pp.639-739.

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