- Astaburuaga , M.A. , Fernandez , C. and Menzala , G.P. 1988 . Huygens’ principle and semilinear wave equation . Comput. Math. Appl. , 15 : 603 – 609 .
- Bardos , C. , Lebeau , G. and Rauch , J. 1988 . Un example d'utilisation des notions de propagation pour le contrôle et la stabilisation des problémes hyperbpliques . Rend. Sem. Mat. Univ. Pol. Torino , 15 : 11 – 32 . Fasc. Spec.
- Courant , R. and Hilbert , D. 1962 . Methods of Mathematical Physics , Vol. II , New York : Interscience .
- Fabre , C. , Puel , J P. and Zuazua , E. 1995 . “ On the density of the range of the semigroup for semilinear heat equations, in Collection ” . In Control and Optimal Design of Distributed Parameter Systems, IMA Vol. Appl. Math. , Vol. 70 , New-York : Springer .
- Günther , P. 1965 . Ein beispiel einer nichttrivialen Huygensscher differentialgleichungen mit vier unabhängigen variablen . Arch. Rat. Mech. Anal. , 2 : 103 – 106 .
- Hadamard , J. 1923 . Lectures on Cauchy's Problem in Linear Partial Differential Equations , Yale University Press .
- Haraux , A. 1987 . Semi-Linear Hyperbolic Problems in Bounded Domains, Mathematical Reports , Vol. 3 , London : Harwood . Part 1
- Ibragimov , N.H. and Mamontov , E.V. 1970 . Sur le probléme de J. Hadamard relatif à la diffusion des ondes , Vol. t. 270 , 456 – 458 . Paris : C.R. Acad. Sci. .
- Ibragimov , N.H. and Mamontov , E.V. 1977 . On Cauchy's problem for . Matem. Sbornik , 102 : 391 – 409 .
- Ladyzhenskaya , O.H. 1985 . The Boundary Value Problems of Mathematical Physics , New-York : Springer-Verlag .
- Lagnese , J.E. 1965 . A new differential operator of the pure wave type . J. Diff. Equat. , 1 : 171 – 187 .
- Lagnese , J.E. 1968 . A solution of Hadamard's problem for a restricted class of operators . Proc. Amer. Math. Soc. , 19 : 981 – 988 .
- Lagnese , J.E. 1969 . The Structure of a class of Huygens’ operators . J. Mech. Math. , 18 : 1195 – 1201 .
- Lagnese , J.E. 1977 . Boundary value control of a class of hyperbolic equations in a general region . SIAM J. Control Opt. , 15 : 973 – 983 .
- Lagnese , J.E. 1978 . Exact boundary value controllability of a class of hyperbolic equations . SIAM J. Control Opt. , 16 : 1000 – 1017 .
- Lagnese , J.E. 1983 . Control of wave processes with distributed controls supported on subregion . SIAM J. Control Opt. , 21 : 68 – 85 .
- Lagnese , J.E. and Stellmacher , K.L. 1967 . A method of generation classes of Huygens’ operators . J. Mech. Math. , 17 : 461 – 472 .
- Lasiecka , I. and Triggiani , R. 1991 . Exact controllability of semilinear abstract systems with application to waves and plates boundary control problems . Appl. Math. Optim. , 23 : 109 – 154 .
- Littman , W. 1987 . “ Near optimal time boundary controllability for a class of hyperbolic equations ” . In Control problems for Systems Described by Partial Differetial Equations , Edited by: Lasiecka , I. and Triggiani , R. Vol. 138 , 307 – 312 . Berlin : Springer-Verlag . Lect. Notes in Control and Inform. Sci.
- Oganesyan , A.O. 1991 . Construction of hyperbolic equations with variable coefficients satisfying Huygen’ principle . Soviet Math. Dokl. , 42 : 600 – 603 .
- Russell , D.L. 1973 . a unified boundary controllability for hyperbolic and parabolic partial differential equations . Studies, Appl. Math. , 52 : 189 – 211 .
- Schwartz , J.T. 1969 . Nonlinear Functional Analysis, Notes on Mathematical and its applications , New-York : Gordon and Breach .
- Stellmacher , K.L. 1953 . Ein beispiel einer Huygensschen differentiagle . Nachr. Akad. Wiss., Göttingen, Math, Phys. Kl. , 10 : 133 – 138 .
- Stellmacher , K.L. 1955 . Einè klasse Huygensscher differentialgleichungen und ihre integration . Math. Ann. , 130 : 219 – 233 .
- Zuazua , E. 1990 . Exact controllability for the semilinear wave equation . J. Math. pures et appl. , 69 : 1 – 31 .
Exact controllability of second-order hyperbolic equations with impulse controls
Reprints and Corporate Permissions
Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?
To request a reprint or corporate permissions for this article, please click on the relevant link below:
Academic Permissions
Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?
Obtain permissions instantly via Rightslink by clicking on the button below:
If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.
Related research
People also read lists articles that other readers of this article have read.
Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.
Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.