Boundary control problem for the one-dimensional Klein-Gordon-Fock equation with a variable coefficient: The case of control by displacements at two endpoints
We consider the problem of boundary control by displacements at two points x = 0 and x = l of a process described by the Klein-Gordon-Fock equation with a variable coefficient on the finite interval 0 ≤ x ≤ l . For the critical time interval T = l , we obtain a necessary and sufficient condition for...
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| Veröffentlicht in: | Differential equations 2013-08, Vol.49 (8), p.1006-1017 |
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| container_title | Differential equations |
| container_volume | 49 |
| creator | Abdukarimov, M. F. Kritskov, L. V. |
| description | We consider the problem of boundary control by displacements at two points
x
= 0 and
x
=
l
of a process described by the Klein-Gordon-Fock equation with a variable coefficient on the finite interval 0 ≤
x
≤
l
. For the critical time interval
T
=
l
, we obtain a necessary and sufficient condition for the existence of unique boundary functions
u
(0,
t
) = µ(
t
) and
u
(
l, t
) =
ν
(
t
) bringing the system from an arbitrary initial state at
t
= 0 into an arbitrary terminal state at
t
=
T
. |
| doi_str_mv | 10.1134/S0012266113080090 |
| format | Article |
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x
= 0 and
x
=
l
of a process described by the Klein-Gordon-Fock equation with a variable coefficient on the finite interval 0 ≤
x
≤
l
. For the critical time interval
T
=
l
, we obtain a necessary and sufficient condition for the existence of unique boundary functions
u
(0,
t
) = µ(
t
) and
u
(
l, t
) =
ν
(
t
) bringing the system from an arbitrary initial state at
t
= 0 into an arbitrary terminal state at
t
=
T
.</description><identifier>ISSN: 0012-2661</identifier><identifier>EISSN: 1608-3083</identifier><identifier>DOI: 10.1134/S0012266113080090</identifier><language>eng</language><publisher>Boston: Springer US</publisher><subject>Boundaries ; Boundary value problems ; Control Theory ; Difference and Functional Equations ; Differential equations ; Interval arithmetic ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Ordinary Differential Equations ; Partial Differential Equations ; Studies</subject><ispartof>Differential equations, 2013-08, Vol.49 (8), p.1006-1017</ispartof><rights>Pleiades Publishing, Ltd. 2013</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c349t-95741dac7d5a3e5fb89c22b6351cc58bf2dadb7dd2be0c8f51e41eb0ab45b4a73</citedby><cites>FETCH-LOGICAL-c349t-95741dac7d5a3e5fb89c22b6351cc58bf2dadb7dd2be0c8f51e41eb0ab45b4a73</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1134/S0012266113080090$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S0012266113080090$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Abdukarimov, M. F.</creatorcontrib><creatorcontrib>Kritskov, L. V.</creatorcontrib><title>Boundary control problem for the one-dimensional Klein-Gordon-Fock equation with a variable coefficient: The case of control by displacements at two endpoints</title><title>Differential equations</title><addtitle>Diff Equat</addtitle><description>We consider the problem of boundary control by displacements at two points
x
= 0 and
x
=
l
of a process described by the Klein-Gordon-Fock equation with a variable coefficient on the finite interval 0 ≤
x
≤
l
. For the critical time interval
T
=
l
, we obtain a necessary and sufficient condition for the existence of unique boundary functions
u
(0,
t
) = µ(
t
) and
u
(
l, t
) =
ν
(
t
) bringing the system from an arbitrary initial state at
t
= 0 into an arbitrary terminal state at
t
=
T
.</description><subject>Boundaries</subject><subject>Boundary value problems</subject><subject>Control Theory</subject><subject>Difference and Functional Equations</subject><subject>Differential equations</subject><subject>Interval arithmetic</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Ordinary Differential Equations</subject><subject>Partial Differential Equations</subject><subject>Studies</subject><issn>0012-2661</issn><issn>1608-3083</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>BENPR</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNp1kclKBTEQRYMo-Bw-wF3AjZvWpDvpwZ2KEwou1HWToaLRfskzSSv-jN9qmiciiqtQuefeoqoQ2qFkn9KKHdwSQsuyrnNBWkI6soJmtCZtkctqFc0muZj0dbQR4xPJSEP5DH0c-9FpEd6x8i4FP-BF8HKAOTY-4PQI2DsotJ2Di9Y7MeCrAawrzn3Q3hVnXj1jeBlFyiJ-s-kRC_wqghU5I0eCMVZZcOkQ3-UsJWIONN-95DvWNi4GoSA3SBGLhNObx-D0wtv8sYXWjBgibH-9m-j-7PTu5KK4vjm_PDm6LlTFulR0vGFUC9VoLirgRradKktZV5wqxVtpSi20bLQuJRDVGk6BUZBESMYlE021ifaWuXn6lxFi6uc2KhgG4cCPsaes4ZyRup3Q3V_okx9D3sxEsbbjddt1maJLSgUfYwDTL4Kd5z33lPTTxfo_F8uecumJmXUPEH4k_2v6BIAcmww</recordid><startdate>20130801</startdate><enddate>20130801</enddate><creator>Abdukarimov, M. 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F. ; Kritskov, L. V.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c349t-95741dac7d5a3e5fb89c22b6351cc58bf2dadb7dd2be0c8f51e41eb0ab45b4a73</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Boundaries</topic><topic>Boundary value problems</topic><topic>Control Theory</topic><topic>Difference and Functional Equations</topic><topic>Differential equations</topic><topic>Interval arithmetic</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Ordinary Differential Equations</topic><topic>Partial Differential Equations</topic><topic>Studies</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Abdukarimov, M. F.</creatorcontrib><creatorcontrib>Kritskov, L. 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F.</au><au>Kritskov, L. V.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Boundary control problem for the one-dimensional Klein-Gordon-Fock equation with a variable coefficient: The case of control by displacements at two endpoints</atitle><jtitle>Differential equations</jtitle><stitle>Diff Equat</stitle><date>2013-08-01</date><risdate>2013</risdate><volume>49</volume><issue>8</issue><spage>1006</spage><epage>1017</epage><pages>1006-1017</pages><issn>0012-2661</issn><eissn>1608-3083</eissn><abstract>We consider the problem of boundary control by displacements at two points
x
= 0 and
x
=
l
of a process described by the Klein-Gordon-Fock equation with a variable coefficient on the finite interval 0 ≤
x
≤
l
. For the critical time interval
T
=
l
, we obtain a necessary and sufficient condition for the existence of unique boundary functions
u
(0,
t
) = µ(
t
) and
u
(
l, t
) =
ν
(
t
) bringing the system from an arbitrary initial state at
t
= 0 into an arbitrary terminal state at
t
=
T
.</abstract><cop>Boston</cop><pub>Springer US</pub><doi>10.1134/S0012266113080090</doi><tpages>12</tpages></addata></record> |
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| ispartof | Differential equations, 2013-08, Vol.49 (8), p.1006-1017 |
| issn | 0012-2661 1608-3083 |
| language | eng |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Boundaries Boundary value problems Control Theory Difference and Functional Equations Differential equations Interval arithmetic Mathematical analysis Mathematics Mathematics and Statistics Ordinary Differential Equations Partial Differential Equations Studies |
| title | Boundary control problem for the one-dimensional Klein-Gordon-Fock equation with a variable coefficient: The case of control by displacements at two endpoints |
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