Remarks on Controllability of Second Order Evolution Equations in Hilbert Spaces

Previous article Next article Remarks on Controllability of Second Order Evolution Equations in Hilbert SpacesKunio TsujiokaKunio Tsujiokahttps://doi.org/10.1137/0308005PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] H. O. Fattorini, A. V. Balakrishnan and , L. W. Neustadt, Controllability of higher order linear systemsMathematical Theory of Control (Proc. Conf., Los Angeles, Calif., 1967), Academic Press, New York, 1967, 301–311 MR0258493 0225.93003 Google Scholar[2] H. O. Fattorini, On complete controllability of linear systems, J. Differential Equations, 3 (1967), 391–402 10.1016/0022-0396(67)90039-3 MR0212322 0155.15903 CrossrefISIGoogle Scholar[3] Teruo Ushijima, Note on the integration of the wave equation, Sci. Papers College Gen. Ed. Univ. Tokyo, 17 (1967), 155–159 MR0226231 0157.17202 Google Scholar[4] Kôsaku Yosida, An operator-theoretical integration of the wave equation, J. Math. Soc. Japan, 8 (1956), 79–92 MR0107085 0071.09202 CrossrefGoogle Scholar[5] Kôsaku Yosida, Functional analysis, Die Grundlehren der Mathematischen Wissenschaften, Band 123, Academic Press Inc., New York, 1965xi+458 MR0180824 0126.11504 CrossrefGoogle Scholar[6] Nelson Dunford and , Jacob T. Schwartz, Linear operators. Part II: Spectral theory. Self adjoint operators in Hilbert space, With the assistance of William G. Bade and Robert G. Bartle, Interscience Publishers John Wiley & Sons New York-London, 1963ix+pp. 859–1923+7 MR0188745 0128.34803 Google Scholar[7] David L. Russell, Nonharmonic Fourier series in the control theory of distributed parameter systems, J. Math. Anal. Appl., 18 (1967), 542–560 10.1016/0022-247X(67)90045-5 MR0211044 0158.10201 CrossrefISIGoogle Scholar[8A] L. Schwartz, Théorie des distributions. Tome I, Actualités Sci. Ind., no. 1091 = Publ. Inst. Math. Univ. Strasbourg 9, Hermann & Cie., Paris, 1950, 148– MR0035918 0037.07301 Google Scholar[8B] Laurent Schwartz, Théorie des distributions. Tome II, Actualités Sci. Ind., no. 1122 = Publ. Inst. Math. Univ. Strasbourg 10, Hermann & Cie., Paris, 1951, 169– MR0041345 0042.11405 Google Scholar[9] Francesco Giacomo Tricomi, Differential equations, Translated by Elizabeth A. McHarg, Hafner Publishing Co., New York, 1961x+273 MR0138812 0101.05904 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails The Control Transmutation Method and the Cost of Fast ControlsLuc Miller26 July 2006 | SIAM Journal on Control and Optimization, Vol. 45, No. 2AbstractPDF (172 KB)Some Problems in the Control of Distributed Systems, and Their Numerical SolutionGreg Knowles18 July 2006 | SIAM Journal on Control and Optimization, Vol. 17, No. 1AbstractPDF (1597 KB)On the Relationship between First and Second Order Controllable Systems in Banach SpacesRoberto Triggiani1 August 2006 | SIAM Journal on Control and Optimization, Vol. 16, No. 6AbstractPDF (1497 KB)Modal Control of Certain Flexible Dynamic SystemsMark J. Balas18 July 2006 | SIAM Journal on Control and Optimization, Vol. 16, No. 3AbstractPDF (1252 KB)Time Optimal Control of Infinite-Dimensional SystemsG. Knowles18 July 2006 | SIAM Journal on Control and Optimization, Vol. 14, No. 5AbstractPDF (1501 KB)Boundary Control of Parabolic Differential Equations in Arbitrary Dimensions: Supremum-Norm ProblemsKlaus Glashoff and Norbert Weck18 July 2006 | SIAM Journal on Control and Optimization, Vol. 14, No. 4AbstractPDF (1514 KB)Controllability for Partial Differential Equations of Parabolic TypeYoshiyuki Sakawa18 July 2006 | SIAM Journal on Control, Vol. 12, No. 3AbstractPDF (818 KB) Volume 8, Issue 1| 1970SIAM Journal on Control History Submitted:28 May 1968Accepted:16 June 1969Published online:18 July 2006 InformationCopyright © 1970 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0308005Article page range:pp. 90-99ISSN (print):0036-1402Publisher:Society for Industrial and Applied Mathematics