{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,12]],"date-time":"2023-09-12T16:32:22Z","timestamp":1694536342551},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2012,5]]},"DOI":"10.1007\/s10589-010-9375-x","type":"journal-article","created":{"date-parts":[[2010,11,19]],"date-time":"2010-11-19T17:18:27Z","timestamp":1290187107000},"page":"147-179","source":"Crossref","is-referenced-by-count":11,"title":["Sensitivity analysis of hyperbolic optimal control problems"],"prefix":"10.1007","volume":"52","author":[{"given":"Adam","family":"Kowalewski","sequence":"first","affiliation":[]},{"given":"Irena","family":"Lasiecka","sequence":"additional","affiliation":[]},{"given":"Jan","family":"Soko\u0142owski","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2010,11,20]]},"reference":[{"key":"9375_CR1","doi-asserted-by":"crossref","first-page":"1194","DOI":"10.1137\/S0363012901384247","volume":"41","author":"H. Ammari","year":"2002","unstructured":"Ammari, H.: An inverse initial boundary value problem for the wave equation in the presence of imperfections of small volume. SIAM J. Control Optim. 41, 1194\u20131211 (2002)","journal-title":"SIAM J. Control Optim."},{"key":"9375_CR2","first-page":"1011","volume":"137","author":"F.A. Berezin","year":"1961","unstructured":"Berezin, F.A., Faddeev, L.D.: Remark on the Schr\u00f6dinger equation with singular potential. Dokl. Akad. Nauk SSSR 137, 1011\u20131014 (1961). (Engl transl. in Soviet Math. Dokl. 2, 372\u2013375 (1961))","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"9375_CR3","doi-asserted-by":"crossref","first-page":"3925","DOI":"10.1137\/08073367X","volume":"48","author":"G. Cardone","year":"2010","unstructured":"Cardone, G., Nazarov, S.A., Soko\u0142owski, J.: Asymptotic analysis, polarization matrices and topological derivatives for piezoelectric materials with small voids. SIAM J. Control Optim. 48, 3925\u20133961 (2010)","journal-title":"SIAM J. Control Optim."},{"key":"9375_CR4","doi-asserted-by":"crossref","unstructured":"Fr\u00e9miot, G., Horn, W., Laurain, A., Rao, M., Soko\u0142owski, J.: On the analysis of boundary value problems in nonsmooth domains. Dissertat. Math. 462 (2009)","DOI":"10.4064\/dm462-0-1"},{"key":"9375_CR5","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1007\/BF01299546","volume":"2","author":"E. Hendrickson","year":"1993","unstructured":"Hendrickson, E., Lasiecka, I.: Numerical approximations and regularizations of Riccati equations arising in hyperbolic dynamics with unbounded control operators. Comput. Optim. Appl. 2, 343\u2013390 (1993)","journal-title":"Comput. Optim. Appl."},{"key":"9375_CR6","first-page":"101","volume":"1","author":"E. Hendrickson","year":"1995","unstructured":"Hendrickson, E., Lasiecka, I.: Finite dimensional approximations of boundary control problems arising in partially observed hyperbolic systems. Dyn. Contin. Discrete Impuls. Syst. 1, 101\u2013142 (1995)","journal-title":"Dyn. Contin. Discrete Impuls. Syst."},{"key":"9375_CR7","volume-title":"The Analysis of Linear Partial Differential Operators","author":"L. Hormander","year":"1985","unstructured":"Hormander, L.: The Analysis of Linear Partial Differential Operators, vol.\u00a0III. Springer, Berlin (1985)"},{"key":"9375_CR8","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1023\/A:1020528902875","volume":"23","author":"L. Jackowska","year":"2002","unstructured":"Jackowska, L., Soko\u0142owski, J., \u017bochowski, A., Henrot, A.: On numerical solution of shape inverse problems. Comput. Optim. Appl. 23, 231\u2013255 (2002)","journal-title":"Comput. Optim. Appl."},{"key":"9375_CR9","first-page":"49","volume":"40","author":"Yu.E. Karpeshina","year":"1986","unstructured":"Karpeshina, Yu.E., Pavlov, B.S.: Interaction of the zero radius for the biharmonic and the polyharmonic equation. Mat. Zametki 40, 49\u201359 (1986) (in Russian)","journal-title":"Mat. Zametki"},{"key":"9375_CR10","doi-asserted-by":"crossref","first-page":"1718","DOI":"10.1016\/j.jmps.2009.07.003","volume":"57","author":"A. Khludnev","year":"2009","unstructured":"Khludnev, A., Novotny, A., Soko\u0142owski, J., \u017bochowski, A.: Shape and topology sensitivity analysis for cracks in elastic bodies on boundaries of rigid inclusions. J. Mech. Phys. Solids 57, 1718\u20131732 (2009)","journal-title":"J. Mech. Phys. Solids"},{"key":"9375_CR11","doi-asserted-by":"crossref","first-page":"3071","DOI":"10.1090\/S0002-9939-05-08063-9","volume":"133","author":"P. Kurasov","year":"2005","unstructured":"Kurasov, P., Posilicano, A.: Finite speed of propagation and local boundary conditions for wave equations with point interactions. Proc. Am. Math. Soc. 133, 3071\u20133078 (2005)","journal-title":"Proc. Am. Math. Soc."},{"key":"9375_CR12","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970821","volume-title":"Stabilization of Thin Plates","author":"J. Lagnese","year":"1989","unstructured":"Lagnese, J.: Stabilization of Thin Plates. SIAM, Philadelphia (1989)"},{"key":"9375_CR13","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-0348-7885-2","volume-title":"Domain Decomposition Methods in Optimal Control of Partial Differential Equations","author":"J. Lagnese","year":"2004","unstructured":"Lagnese, J., Leugering, G.: Domain Decomposition Methods in Optimal Control of Partial Differential Equations. Birkh\u00e4user, Basel (2004)"},{"key":"9375_CR14","volume-title":"Fundamentals of Modern Potential Theory","author":"N.S. Landkof","year":"1966","unstructured":"Landkof, N.S.: Fundamentals of Modern Potential Theory. Nauka, Moscow (1966) (in Russian)"},{"key":"9375_CR15","series-title":"CBMS-SIAM-NSF Lecture Notes","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898717099","volume-title":"Control Theory for Coupled PDE\u2019s","author":"I. Lasiecka","year":"2002","unstructured":"Lasiecka, I.: Control Theory for Coupled PDE\u2019s. CBMS-SIAM-NSF Lecture Notes. SIAM, Philadelphia (2002)"},{"key":"9375_CR16","first-page":"149","volume":"65","author":"I. Lasiecka","year":"1986","unstructured":"Lasiecka, I., Lions, J.L., Triggiani, R.: Non-homogeneous boundary value problems for second order hyperbolic operators. J. Math. Pures Appl. 65, 149\u2013192 (1986)","journal-title":"J. Math. Pures Appl."},{"key":"9375_CR17","doi-asserted-by":"crossref","first-page":"1128","DOI":"10.1137\/0329060","volume":"29","author":"I. Lasiecka","year":"1991","unstructured":"Lasiecka, I., Soko\u0142owski, J.: Sensitivity analysis of constrained optimal control problem for wave equation. SIAM J. Control Optim. 29, 1128\u20131149 (1991)","journal-title":"SIAM J. Control Optim."},{"key":"9375_CR18","first-page":"1128","volume":"CLVII","author":"I. Lasiecka","year":"1990","unstructured":"Lasiecka, I., Triggiani, R.: Sharp regularity results for second order hyperbolic equations of Neumann type. Ann Mat. Pura Appl. CLVII, 1128\u20131149 (1990)","journal-title":"Ann Mat. Pura Appl."},{"key":"9375_CR19","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1016\/0022-0396(91)90106-J","volume":"94","author":"I. Lasiecka","year":"1991","unstructured":"Lasiecka, I., Triggiani, R.: Regularity theory of hyperbolic equations with non-homogeneous Neumann boundary conditions. J. Differ. Equ. 94, 112\u2013164 (1991)","journal-title":"J. Differ. Equ."},{"key":"9375_CR20","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511574801","volume-title":"Control Theory for Partial Differential Equations","author":"I. Lasiecka","year":"2000","unstructured":"Lasiecka, I., Triggiani, R.: Control Theory for Partial Differential Equations. Cambridge University Press, Cambridge (2000)"},{"key":"9375_CR21","series-title":"Contemporary Math.","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1090\/conm\/268\/04315","volume-title":"Differential Geometric Methods in the Control of Partial Differential Equations","author":"I. Lasiecka","year":"2000","unstructured":"Lasiecka, I., Triggiani, R., Zhang, X.: In: Differential Geometric Methods in the Control of Partial Differential Equations. Contemporary Math., pp. 227\u2013327. AMS, Providence (2000)"},{"key":"9375_CR22","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-65024-6","volume-title":"Optimal Control of Systems Governed by Partial Differential Equations","author":"J.L. Lions","year":"1971","unstructured":"Lions, J.L.: Optimal Control of Systems Governed by Partial Differential Equations. Springer, Berlin (1971)"},{"key":"9375_CR23","volume-title":"Non-Homogeneous Boundary Value Problems and Applications, vols. 1 and 2","author":"J.L. Lions","year":"1972","unstructured":"Lions, J.L., Magenes, E.: Non-Homogeneous Boundary Value Problems and Applications, vols. 1 and 2. Springer, Berlin (1972)"},{"key":"9375_CR24","doi-asserted-by":"crossref","unstructured":"Malanowski, K.: Stability and sensitivity analysis for optimal control problems with control-state constraints. Dissertat. Math. 394 (2001)","DOI":"10.4064\/dm394-0-1"},{"key":"9375_CR25","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1016\/0022-247X(86)90213-1","volume":"120","author":"K. Malanowski","year":"1986","unstructured":"Malanowski, K., Soko\u0142owski, J.: Sensitivity of solutions to convex, control constrained optimal control problems for distributed parameter systems. J. Math. Anal. Appl. 120, 240\u2013263 (1986)","journal-title":"J. Math. Anal. Appl."},{"key":"9375_CR26","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-0348-8432-7","volume-title":"Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains","author":"V. Maz\u2019ya","year":"2000","unstructured":"Maz\u2019ya, V., Nazarov, S., Plamenevskij, B.: Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains, vol.\u00a01. Birkh\u00e4user, Basel (2000)"},{"key":"9375_CR27","first-page":"224","volume":"137","author":"S.A. Nazarov","year":"1988","unstructured":"Nazarov, S.A.: Self-adjoint extensions of the Dirichlet problem operator in weighted function spaces. Mat. Sb. 137, 224\u2013241 (1988) (English transl.: Math. USSR Sbornik 65, 229\u2013247 (1990))","journal-title":"Mat. Sb."},{"key":"9375_CR28","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1090\/trans2\/193\/05","volume":"198","author":"S.A. Nazarov","year":"1999","unstructured":"Nazarov, S.A.: Asymptotic conditions at a point, self-adjoint extensions of operators and the method of matched asymptotic expansions. Am. Math. Soc. Transl. 198, 77\u2013125 (1999)","journal-title":"Am. Math. Soc. Transl."},{"key":"9375_CR29","first-page":"39","volume":"12","author":"S.A. Nazarov","year":"2005","unstructured":"Nazarov, S.A., Slutskij, A.S., Soko\u0142owski, J.: Topological derivative of the energy functional due to formation of a thin ligament on a spatial body. Acta Univ. Lodz., Folia Math. 12, 39\u201372 (2005)","journal-title":"Acta Univ. Lodz., Folia Math."},{"key":"9375_CR30","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/S0021-7824(03)00004-7","volume":"82","author":"S.A. Nazarov","year":"2003","unstructured":"Nazarov, S.A., Soko\u0142owski, J.: Asymptotic analysis of shape functionals. J. Math. Pures Appl. 82, 125\u2013196 (2003)","journal-title":"J. Math. Pures Appl."},{"key":"9375_CR31","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1016\/j.crme.2003.07.003","volume":"331","author":"S.A. Nazarov","year":"2003","unstructured":"Nazarov, S.A., Soko\u0142owski, J.: Self-adjoint extensions of differential operators in application to shape optimization. C. R., M\u00e9c. 331, 667\u2013672 (2003)","journal-title":"C. R., M\u00e9c."},{"key":"9375_CR32","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1023\/B:SIMJ.0000021290.61807.4b","volume":"45","author":"S.A. Nazarov","year":"2004","unstructured":"Nazarov, S.A., Soko\u0142owski, J.: The topological derivative of the Dirichlet integral due to formation of a thin ligament. Sib. Math. J. 45, 341\u2013355 (2004)","journal-title":"Sib. Math. J."},{"key":"9375_CR33","doi-asserted-by":"crossref","first-page":"237","DOI":"10.4064\/ba52-3-4","volume":"52","author":"S.A. Nazarov","year":"2004","unstructured":"Nazarov, S.A., Soko\u0142owski, J.: Self-adjoint extensions for elasticity system in application to shape optimization. Bull. Pol. Acad. Sci., Math. 52, 237\u2013248 (2004)","journal-title":"Bull. Pol. Acad. Sci., Math."},{"key":"9375_CR34","doi-asserted-by":"crossref","first-page":"879","DOI":"10.1007\/s10114-005-0652-z","volume":"22","author":"S.A. Nazarov","year":"2006","unstructured":"Nazarov, S.A., Soko\u0142owski, J.: Self-adjoint extensions for the Neumann Laplacian and applications. Acta Math. Sin. 22, 879\u2013906 (2006)","journal-title":"Acta Math. Sin."},{"key":"9375_CR35","doi-asserted-by":"crossref","first-page":"189","DOI":"10.3233\/ASY-2010-0989","volume":"68","author":"S.A. Nazarov","year":"2010","unstructured":"Nazarov, S.A., Specovius-Neugebauer, M., Soko\u0142owski, J.: Polarization matrices in anisotropic elasticity. Asymptot. Anal. 68, 189\u2013221 (2010)","journal-title":"Asymptot. Anal."},{"key":"9375_CR36","first-page":"99","volume":"42","author":"B.S. Pavlov","year":"1987","unstructured":"Pavlov, B.S.: The theory of extension and explicitly soluble models. Usp. Mat. Nauk 42, 99\u2013131 (1987) (Engl. transl. Soviet Math. Surveys 42, 127\u2013168 (1987))","journal-title":"Usp. Mat. Nauk"},{"key":"9375_CR37","doi-asserted-by":"crossref","DOI":"10.1515\/9781400882663","volume-title":"Isoperimetric Inequalities in Mathematical Physics","author":"G. P\u00f3lya","year":"1951","unstructured":"P\u00f3lya, G., Szeg\u00f6, G.: Isoperimetric Inequalities in Mathematical Physics. Princeton University Press, Princeton (1951)"},{"key":"9375_CR38","volume-title":"Hyperbolic Boundary Value Problems","author":"R. Sakamoto","year":"1982","unstructured":"Sakamoto, R.: Hyperbolic Boundary Value Problems. Cambridge University Press, Cambridge (1982)"},{"key":"9375_CR39","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1007\/BF01442201","volume":"13","author":"J. Soko\u0142owski","year":"1985","unstructured":"Soko\u0142owski, J.: Differential stability of solutions to constrained optimization problems. Appl. Math. Optim. 13, 97\u2013115 (1985)","journal-title":"Appl. Math. Optim."},{"key":"9375_CR40","doi-asserted-by":"crossref","first-page":"1542","DOI":"10.1137\/0325085","volume":"25","author":"J. Soko\u0142owski","year":"1987","unstructured":"Soko\u0142owski, J.: Sensitivity analysis of control constrained optimal control problems for distributed parameter systems. SIAM J. Control Optim. 25, 1542\u20131556 (1987)","journal-title":"SIAM J. Control Optim."},{"key":"9375_CR41","doi-asserted-by":"crossref","first-page":"763","DOI":"10.1137\/0326045","volume":"26","author":"J. Soko\u0142owski","year":"1988","unstructured":"Soko\u0142owski, J.: Shape sensitivity analysis of boundary optimal control problems for parabolic systems. SIAM J. Control Optim. 26, 763\u2013787 (1988)","journal-title":"SIAM J. Control Optim."},{"key":"9375_CR42","doi-asserted-by":"crossref","first-page":"1251","DOI":"10.1137\/S0363012997323230","volume":"37","author":"J. Soko\u0142owski","year":"1999","unstructured":"Soko\u0142owski, J., \u017bochowski, A.: On topological derivative in shape optimization. SIAM J. Control Optim. 37, 1251\u20131272 (1999)","journal-title":"SIAM J. Control Optim."},{"key":"9375_CR43","first-page":"611","volume":"28","author":"J. Soko\u0142owski","year":"1999","unstructured":"Soko\u0142owski, J., \u017bochowski, A.: Topological derivative for optimal control problems. Control Cybern. 28, 611\u2013626 (1999)","journal-title":"Control Cybern."},{"key":"9375_CR44","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1088\/0266-5611\/15\/1\/016","volume":"15","author":"J. Soko\u0142owski","year":"1999","unstructured":"Soko\u0142owski, J., \u017bochowski, A.: Topological derivatives for elliptic problems. Inverse Probl. 15, 123\u2013134 (1999)","journal-title":"Inverse Probl."},{"key":"9375_CR45","doi-asserted-by":"crossref","first-page":"1198","DOI":"10.1137\/S0363012901384430","volume":"42","author":"J. Soko\u0142owski","year":"2003","unstructured":"Soko\u0142owski, J., \u017bochowski, A.: Optimality conditions for simultaneous topology and shape optimization. SIAM J. Control Optim. 42, 1198\u20131221 (2003)","journal-title":"SIAM J. Control Optim."},{"key":"9375_CR46","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1007\/s00211-005-0635-0","volume":"102","author":"J. Soko\u0142owski","year":"2005","unstructured":"Soko\u0142owski, J., \u017bochowski, A.: Modelling of topological derivatives for contact problems. Numer. Math. 102, 145\u2013179 (2005)","journal-title":"Numer. Math."},{"key":"9375_CR47","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1016\/j.enganabound.2007.08.013","volume":"32","author":"J. Soko\u0142owski","year":"2008","unstructured":"Soko\u0142owski, J., \u017bochowski, A.: Asymptotic analysis and topological derivatives for shape and topology optimization of elasticity problems in two spatial dimensions. Eng. Anal. Bound. Elem. 32, 533\u2013544 (2008)","journal-title":"Eng. Anal. Bound. Elem."},{"key":"9375_CR48","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-58106-9","volume-title":"Introduction to Shape Optimization. Shape Sensitivity Analysis","author":"J. Soko\u0142owski","year":"1992","unstructured":"Soko\u0142owski, J., Zolesio, J.-P.: Introduction to Shape Optimization. Shape Sensitivity Analysis. Springer, Berlin (1992)"}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.springerlink.com\/index\/pdf\/10.1007\/s10589-010-9375-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,6,13]],"date-time":"2020-06-13T23:17:29Z","timestamp":1592090249000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-010-9375-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,11,20]]},"references-count":48,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,5]]}},"alternative-id":["9375"],"URL":"https:\/\/doi.org\/10.1007\/s10589-010-9375-x","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,11,20]]}}}