Factor spaces and implications on Kirchhoff equations with clamped boundary conditions
We consider mixed problems for the Kirchhoff elastic and thermoelastic systems, subject to boundary control in the clamped boundary conditions BC (clamped control). If w denotes the elastic displacement and θ the temperature, we establish sharp regularity of {w,wt,wtt} in the elastic case, and of {w...
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| Format: | Article |
| Language: | English |
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Wiley
2001-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/S1085337501000586 |
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| _version_ | 1849412070569672704 |
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| author | Irena Lasiecka Roberto Triggiani |
| author_facet | Irena Lasiecka Roberto Triggiani |
| author_sort | Irena Lasiecka |
| collection | DOAJ |
| description | We consider mixed problems for the Kirchhoff elastic and
thermoelastic systems, subject to boundary control in the clamped
boundary conditions BC (clamped control). If w
denotes the
elastic displacement and θ
the temperature, we establish
sharp regularity of {w,wt,wtt}
in the elastic case, and
of {w,wt,wtt,θ}
in the thermoelastic case. Our
results complement those by Lagnese and Lions (1988), where sharp
(optimal) trace regularity results are obtained for the
corresponding boundary homogeneous cases. The passage from the
boundary homogeneous cases to the corresponding mixed problems
involves a duality argument. However, in the present case of
clamped BC, and only in this case, the duality argument in
question is both delicate and technical. In this respect, the
clamped BC are “exceptional” within the set of canonical
BC (hinged, clamped, free BC). Indeed, it produces new phenomena
which are accounted for by introducing new, untraditional factor
(quotient) spaces. These are critical in describing both interior
regularity and exact controllability of mixed elastic and
thermoelastic Kirchhoff problems with clamped controls. |
| format | Article |
| id | doaj-art-5e5ef0edd2ad4e16820bc59c36b04e55 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-5e5ef0edd2ad4e16820bc59c36b04e552025-08-20T03:34:33ZengWileyAbstract and Applied Analysis1085-33751687-04092001-01-016844148810.1155/S1085337501000586Factor spaces and implications on Kirchhoff equations with clamped boundary conditionsIrena Lasiecka0Roberto Triggiani1Department of Mathematics, University of Virginia, Charlottesville, VA 22904, USADepartment of Mathematics, University of Virginia, Charlottesville, VA 22904, USAWe consider mixed problems for the Kirchhoff elastic and thermoelastic systems, subject to boundary control in the clamped boundary conditions BC (clamped control). If w denotes the elastic displacement and θ the temperature, we establish sharp regularity of {w,wt,wtt} in the elastic case, and of {w,wt,wtt,θ} in the thermoelastic case. Our results complement those by Lagnese and Lions (1988), where sharp (optimal) trace regularity results are obtained for the corresponding boundary homogeneous cases. The passage from the boundary homogeneous cases to the corresponding mixed problems involves a duality argument. However, in the present case of clamped BC, and only in this case, the duality argument in question is both delicate and technical. In this respect, the clamped BC are “exceptional” within the set of canonical BC (hinged, clamped, free BC). Indeed, it produces new phenomena which are accounted for by introducing new, untraditional factor (quotient) spaces. These are critical in describing both interior regularity and exact controllability of mixed elastic and thermoelastic Kirchhoff problems with clamped controls.http://dx.doi.org/10.1155/S1085337501000586 |
| spellingShingle | Irena Lasiecka Roberto Triggiani Factor spaces and implications on Kirchhoff equations with clamped boundary conditions Abstract and Applied Analysis |
| title | Factor spaces and implications on Kirchhoff equations with clamped boundary conditions |
| title_full | Factor spaces and implications on Kirchhoff equations with clamped boundary conditions |
| title_fullStr | Factor spaces and implications on Kirchhoff equations with clamped boundary conditions |
| title_full_unstemmed | Factor spaces and implications on Kirchhoff equations with clamped boundary conditions |
| title_short | Factor spaces and implications on Kirchhoff equations with clamped boundary conditions |
| title_sort | factor spaces and implications on kirchhoff equations with clamped boundary conditions |
| url | http://dx.doi.org/10.1155/S1085337501000586 |
| work_keys_str_mv | AT irenalasiecka factorspacesandimplicationsonkirchhoffequationswithclampedboundaryconditions AT robertotriggiani factorspacesandimplicationsonkirchhoffequationswithclampedboundaryconditions |