کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9495505 | 1335135 | 2005 | 37 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A spectral approach for the exact observability of infinite-dimensional systems with skew-adjoint generator
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Let A be a possibly unbounded skew-adjoint operator on the Hilbert space X with compact resolvent. Let C be a bounded operator from D(A) to another Hilbert space Y. We consider the system governed by the state equation zË(t)=Az(t) with the output y(t)=Cz(t). We characterize the exact observability of this system only in terms of C and of the spectral elements of the operator A. The starting point in the proof of this result is a Hautus-type test, recently obtained in Burq and Zworski (J. Amer. Soc. 17 (2004) 443-471) and Miller (J. Funct. Anal. 218 (2) (2005) 425-444). We then apply this result to various systems governed by partial differential equations with observation on the boundary of the domain. The Schrödinger equation, the Bernoulli-Euler plate equation and the wave equation in a square are considered. For the plate and Schrödinger equations, the main novelty brought in by our results is that we prove the exact boundary observability for an arbitrarily small observed part of the boundary. This is done by combining our spectral observability test to a theorem of Beurling on nonharmonic Fourier series and to a new number theoretic result on shifted squares.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 226, Issue 1, 1 September 2005, Pages 193-229
Journal: Journal of Functional Analysis - Volume 226, Issue 1, 1 September 2005, Pages 193-229
نویسندگان
K. Ramdani, T. Takahashi, G. Tenenbaum, M. Tucsnak,