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 Posted: Thu 14:44, 13 Jan 2011 Post subject: stivali ugg Interference for a Class of Wave Equat |
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Interference term with a class of wave equations exact controllability
+ IuId £ = kLr ~ (£) is easy to prove: I2 + IV = flip x '(\2Ecz,[link widoczny dla zalogowanych], one to relaxation cz,[link widoczny dla zalogowanych], a cz, a Ecz, ≥ (T-2L-kLT a nkT a-n-1) E (.) so that s \-=,[link widoczny dla zalogowanych], then the inequality (4) left the establishment, the use of inequality (3), Order \/ 2a's320 Taiyuan University of Science and Technology 2007, positive, and called . T> i II 22 (1 a kL) rY A n then consider the system a Ay + ky = 0, (, t) ∈ force × R? Y = Ov \, Y () = 0, ∈ the solution,, * lJJ ~ JlN (2), easy to prove that A: (u., u) a ((0), (0)) is (force) × L2 (force) to L2 (force) × H (force) isomorphism. According to the principle of Hilbert uniqueness ..., system (1) is controlled precisely zero, zero according to precise control and accurate knowledge to control the equivalence The system (1) is the exact controllability. References: [1] [2] [3] [4] [5] [6] JLLIONS.Exactcontrollability, stabilizability, andperturbationsfordistributedsystem [J]. SiamReview,[link widoczny dla zalogowanych], 1988,30 (1 ) :1-68. KONORNIKV.Exactcontrobilityandstabilizationandthemultipliermethod [M]. Paris, Masson ,1994,7-60. KOMORNKUV.ZUAZUAE.Adirectmethodforboundarystabilizationofthewaveequation [J]. math.PuresetApple ,1990,69:33-54. RUTHF.CurtainHansZartAnintroductiontoinfinite-DimensionalLinearSystemsTheroy [ ,],[[M]. NewyorkSpringer-verlag ,1988,15-40. ExactControllabilityoftheWaveEquationwithInterveneGUOLi ~ un, LILi-ping (TaiyuanUniversityofScienceandTechnology, Taiyuan030024, China) Abstract: Theexactcontrollabilityofthewaveequationwithintervene, rY \Y =, (, t) ∈ F × R 【), (0): Y. , Y (0) = Y,[link widoczny dla zalogowanych], ∈ force isdiscussed. TheexactcontrollabilityofthesystemisverifiedbyusinghibertuniquemethodKeywords: exactcontrollability, waveequation, intervene
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