Approximate solutions to Dirichlet control problems for the wave equation in Sobolev classes and dual observation problems
Abstract Dual control and observation problems for the wave equation with variable coefficients subject to Dirichlet boundary conditions are solved by a variational method. This method was earlier proposed by the author for an approximate analysis of linear equations with nonuniform perturbations of...
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Gespeichert in:
| Autor*in: |
Potapov, M. M. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2006 |
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| Schlagwörter: |
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| Anmerkung: |
© MAIK “Nauka/Interperiodica” 2006 |
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| Übergeordnetes Werk: |
Enthalten in: Computational mathematics and mathematical physics - Nauka/Interperiodica, 1992, 46(2006), 12 vom: Dez., Seite 2092-2109 |
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| Übergeordnetes Werk: |
volume:46 ; year:2006 ; number:12 ; month:12 ; pages:2092-2109 |
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| DOI / URN: |
10.1134/S0965542506120086 |
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OLC2037341652 |
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| 520 | |a Abstract Dual control and observation problems for the wave equation with variable coefficients subject to Dirichlet boundary conditions are solved by a variational method. This method was earlier proposed by the author for an approximate analysis of linear equations with nonuniform perturbations of the operator. Explicit bounds on the constant that are required to implement the method are obtained using the correct solvability property of the dual observation problem. Finite-dimensional approximations of the control and observation problems are obtained by the difference method preserving the duality relation. The convergence of approximate solutions is established in the norms of the corresponding dual spaces. | ||
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| 650 | 4 | |a convergence | |
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10.1134/S0965542506120086 doi (DE-627)OLC2037341652 (DE-He213)S0965542506120086-p DE-627 ger DE-627 rakwb eng 510 VZ Potapov, M. M. verfasserin aut Approximate solutions to Dirichlet control problems for the wave equation in Sobolev classes and dual observation problems 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © MAIK “Nauka/Interperiodica” 2006 Abstract Dual control and observation problems for the wave equation with variable coefficients subject to Dirichlet boundary conditions are solved by a variational method. This method was earlier proposed by the author for an approximate analysis of linear equations with nonuniform perturbations of the operator. Explicit bounds on the constant that are required to implement the method are obtained using the correct solvability property of the dual observation problem. Finite-dimensional approximations of the control and observation problems are obtained by the difference method preserving the duality relation. The convergence of approximate solutions is established in the norms of the corresponding dual spaces. wave equation controllability observability duality finite-dimensional approximation convergence Enthalten in Computational mathematics and mathematical physics Nauka/Interperiodica, 1992 46(2006), 12 vom: Dez., Seite 2092-2109 (DE-627)131059181 (DE-600)1106328-2 (DE-576)029158060 0965-5425 nnns volume:46 year:2006 number:12 month:12 pages:2092-2109 https://doi.org/10.1134/S0965542506120086 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_4311 AR 46 2006 12 12 2092-2109 |
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10.1134/S0965542506120086 doi (DE-627)OLC2037341652 (DE-He213)S0965542506120086-p DE-627 ger DE-627 rakwb eng 510 VZ Potapov, M. M. verfasserin aut Approximate solutions to Dirichlet control problems for the wave equation in Sobolev classes and dual observation problems 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © MAIK “Nauka/Interperiodica” 2006 Abstract Dual control and observation problems for the wave equation with variable coefficients subject to Dirichlet boundary conditions are solved by a variational method. This method was earlier proposed by the author for an approximate analysis of linear equations with nonuniform perturbations of the operator. Explicit bounds on the constant that are required to implement the method are obtained using the correct solvability property of the dual observation problem. Finite-dimensional approximations of the control and observation problems are obtained by the difference method preserving the duality relation. The convergence of approximate solutions is established in the norms of the corresponding dual spaces. wave equation controllability observability duality finite-dimensional approximation convergence Enthalten in Computational mathematics and mathematical physics Nauka/Interperiodica, 1992 46(2006), 12 vom: Dez., Seite 2092-2109 (DE-627)131059181 (DE-600)1106328-2 (DE-576)029158060 0965-5425 nnns volume:46 year:2006 number:12 month:12 pages:2092-2109 https://doi.org/10.1134/S0965542506120086 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_4311 AR 46 2006 12 12 2092-2109 |
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10.1134/S0965542506120086 doi (DE-627)OLC2037341652 (DE-He213)S0965542506120086-p DE-627 ger DE-627 rakwb eng 510 VZ Potapov, M. M. verfasserin aut Approximate solutions to Dirichlet control problems for the wave equation in Sobolev classes and dual observation problems 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © MAIK “Nauka/Interperiodica” 2006 Abstract Dual control and observation problems for the wave equation with variable coefficients subject to Dirichlet boundary conditions are solved by a variational method. This method was earlier proposed by the author for an approximate analysis of linear equations with nonuniform perturbations of the operator. Explicit bounds on the constant that are required to implement the method are obtained using the correct solvability property of the dual observation problem. Finite-dimensional approximations of the control and observation problems are obtained by the difference method preserving the duality relation. The convergence of approximate solutions is established in the norms of the corresponding dual spaces. wave equation controllability observability duality finite-dimensional approximation convergence Enthalten in Computational mathematics and mathematical physics Nauka/Interperiodica, 1992 46(2006), 12 vom: Dez., Seite 2092-2109 (DE-627)131059181 (DE-600)1106328-2 (DE-576)029158060 0965-5425 nnns volume:46 year:2006 number:12 month:12 pages:2092-2109 https://doi.org/10.1134/S0965542506120086 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_4311 AR 46 2006 12 12 2092-2109 |
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10.1134/S0965542506120086 doi (DE-627)OLC2037341652 (DE-He213)S0965542506120086-p DE-627 ger DE-627 rakwb eng 510 VZ Potapov, M. M. verfasserin aut Approximate solutions to Dirichlet control problems for the wave equation in Sobolev classes and dual observation problems 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © MAIK “Nauka/Interperiodica” 2006 Abstract Dual control and observation problems for the wave equation with variable coefficients subject to Dirichlet boundary conditions are solved by a variational method. This method was earlier proposed by the author for an approximate analysis of linear equations with nonuniform perturbations of the operator. Explicit bounds on the constant that are required to implement the method are obtained using the correct solvability property of the dual observation problem. Finite-dimensional approximations of the control and observation problems are obtained by the difference method preserving the duality relation. The convergence of approximate solutions is established in the norms of the corresponding dual spaces. wave equation controllability observability duality finite-dimensional approximation convergence Enthalten in Computational mathematics and mathematical physics Nauka/Interperiodica, 1992 46(2006), 12 vom: Dez., Seite 2092-2109 (DE-627)131059181 (DE-600)1106328-2 (DE-576)029158060 0965-5425 nnns volume:46 year:2006 number:12 month:12 pages:2092-2109 https://doi.org/10.1134/S0965542506120086 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_4311 AR 46 2006 12 12 2092-2109 |
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10.1134/S0965542506120086 doi (DE-627)OLC2037341652 (DE-He213)S0965542506120086-p DE-627 ger DE-627 rakwb eng 510 VZ Potapov, M. M. verfasserin aut Approximate solutions to Dirichlet control problems for the wave equation in Sobolev classes and dual observation problems 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © MAIK “Nauka/Interperiodica” 2006 Abstract Dual control and observation problems for the wave equation with variable coefficients subject to Dirichlet boundary conditions are solved by a variational method. This method was earlier proposed by the author for an approximate analysis of linear equations with nonuniform perturbations of the operator. Explicit bounds on the constant that are required to implement the method are obtained using the correct solvability property of the dual observation problem. Finite-dimensional approximations of the control and observation problems are obtained by the difference method preserving the duality relation. The convergence of approximate solutions is established in the norms of the corresponding dual spaces. wave equation controllability observability duality finite-dimensional approximation convergence Enthalten in Computational mathematics and mathematical physics Nauka/Interperiodica, 1992 46(2006), 12 vom: Dez., Seite 2092-2109 (DE-627)131059181 (DE-600)1106328-2 (DE-576)029158060 0965-5425 nnns volume:46 year:2006 number:12 month:12 pages:2092-2109 https://doi.org/10.1134/S0965542506120086 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_4311 AR 46 2006 12 12 2092-2109 |
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Approximate solutions to Dirichlet control problems for the wave equation in Sobolev classes and dual observation problems |
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Abstract Dual control and observation problems for the wave equation with variable coefficients subject to Dirichlet boundary conditions are solved by a variational method. This method was earlier proposed by the author for an approximate analysis of linear equations with nonuniform perturbations of the operator. Explicit bounds on the constant that are required to implement the method are obtained using the correct solvability property of the dual observation problem. Finite-dimensional approximations of the control and observation problems are obtained by the difference method preserving the duality relation. The convergence of approximate solutions is established in the norms of the corresponding dual spaces. © MAIK “Nauka/Interperiodica” 2006 |
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Abstract Dual control and observation problems for the wave equation with variable coefficients subject to Dirichlet boundary conditions are solved by a variational method. This method was earlier proposed by the author for an approximate analysis of linear equations with nonuniform perturbations of the operator. Explicit bounds on the constant that are required to implement the method are obtained using the correct solvability property of the dual observation problem. Finite-dimensional approximations of the control and observation problems are obtained by the difference method preserving the duality relation. The convergence of approximate solutions is established in the norms of the corresponding dual spaces. © MAIK “Nauka/Interperiodica” 2006 |
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Abstract Dual control and observation problems for the wave equation with variable coefficients subject to Dirichlet boundary conditions are solved by a variational method. This method was earlier proposed by the author for an approximate analysis of linear equations with nonuniform perturbations of the operator. Explicit bounds on the constant that are required to implement the method are obtained using the correct solvability property of the dual observation problem. Finite-dimensional approximations of the control and observation problems are obtained by the difference method preserving the duality relation. The convergence of approximate solutions is established in the norms of the corresponding dual spaces. © MAIK “Nauka/Interperiodica” 2006 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2037341652</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230504115431.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200820s2006 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1134/S0965542506120086</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2037341652</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)S0965542506120086-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Potapov, M. M.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Approximate solutions to Dirichlet control problems for the wave equation in Sobolev classes and dual observation problems</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2006</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© MAIK “Nauka/Interperiodica” 2006</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Dual control and observation problems for the wave equation with variable coefficients subject to Dirichlet boundary conditions are solved by a variational method. This method was earlier proposed by the author for an approximate analysis of linear equations with nonuniform perturbations of the operator. Explicit bounds on the constant that are required to implement the method are obtained using the correct solvability property of the dual observation problem. Finite-dimensional approximations of the control and observation problems are obtained by the difference method preserving the duality relation. 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