L2(Σ)-regularity of the boundary to boundary operator B∗L for hyperbolic and Petrowski PDEs
This paper takes up and thoroughly analyzes a technical mathematical issue in PDE theory, whileas a by-pass productmaking a larger case. The technical issue is the L2(Σ)-regularity of the boundary → boundary operator B∗L for (multidimensional) hyperbolic and Petrowski-type mixed PDEs problems, where...
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| Format: | Article |
| Language: | English |
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Wiley
2003-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/S1085337503305032 |
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| author | I. Lasiecka R. Triggiani |
| author_facet | I. Lasiecka R. Triggiani |
| author_sort | I. Lasiecka |
| collection | DOAJ |
| description | This paper takes up and thoroughly analyzes a technical mathematical issue in PDE theory, whileas a by-pass productmaking a larger case. The technical issue is the L2(Σ)-regularity of the boundary → boundary operator B∗L for (multidimensional) hyperbolic and Petrowski-type mixed PDEs problems, where L is the boundary input → interior solution operator and B is the control operator from the boundary. Both positive and negative classes of
distinctive PDE illustrations are exhibited and proved. The larger case to be made is that hard analysis PDE energy methods are the tools of the tradenot soft analysis methods. This holds true not only to analyze B∗L, but also to establish three inter-related cardinal results: optimal PDE regularity, exact controllability, and uniform stabilization. Thus, the paper takes a critical view on a spate of abstract results in infinite-dimensional systems theory, generated by unnecessarily complicated and highly limited soft methods, with no apparent awareness of the high degree of restriction of the abstract assumptions madefar from necessaryas well as on how to verify them in the case of multidimensional dynamical systems such as PDEs. |
| format | Article |
| id | doaj-art-19c1af3f2a1b41449de1cb12ba445dc0 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-19c1af3f2a1b41449de1cb12ba445dc02025-08-20T02:02:08ZengWileyAbstract and Applied Analysis1085-33751687-04092003-01-012003191061113910.1155/S1085337503305032L2(Σ)-regularity of the boundary to boundary operator B∗L for hyperbolic and Petrowski PDEsI. Lasiecka0R. Triggiani1Department of Mathematics, Kerch of Hall, University of Virginia, Charlottesville 22904, VA, USADepartment of Mathematics, Kerch of Hall, University of Virginia, Charlottesville 22904, VA, USAThis paper takes up and thoroughly analyzes a technical mathematical issue in PDE theory, whileas a by-pass productmaking a larger case. The technical issue is the L2(Σ)-regularity of the boundary → boundary operator B∗L for (multidimensional) hyperbolic and Petrowski-type mixed PDEs problems, where L is the boundary input → interior solution operator and B is the control operator from the boundary. Both positive and negative classes of distinctive PDE illustrations are exhibited and proved. The larger case to be made is that hard analysis PDE energy methods are the tools of the tradenot soft analysis methods. This holds true not only to analyze B∗L, but also to establish three inter-related cardinal results: optimal PDE regularity, exact controllability, and uniform stabilization. Thus, the paper takes a critical view on a spate of abstract results in infinite-dimensional systems theory, generated by unnecessarily complicated and highly limited soft methods, with no apparent awareness of the high degree of restriction of the abstract assumptions madefar from necessaryas well as on how to verify them in the case of multidimensional dynamical systems such as PDEs.http://dx.doi.org/10.1155/S1085337503305032 |
| spellingShingle | I. Lasiecka R. Triggiani L2(Σ)-regularity of the boundary to boundary operator B∗L for hyperbolic and Petrowski PDEs Abstract and Applied Analysis |
| title | L2(Σ)-regularity of the boundary to boundary operator B∗L for hyperbolic and Petrowski PDEs |
| title_full | L2(Σ)-regularity of the boundary to boundary operator B∗L for hyperbolic and Petrowski PDEs |
| title_fullStr | L2(Σ)-regularity of the boundary to boundary operator B∗L for hyperbolic and Petrowski PDEs |
| title_full_unstemmed | L2(Σ)-regularity of the boundary to boundary operator B∗L for hyperbolic and Petrowski PDEs |
| title_short | L2(Σ)-regularity of the boundary to boundary operator B∗L for hyperbolic and Petrowski PDEs |
| title_sort | l2 σ regularity of the boundary to boundary operator b∗l for hyperbolic and petrowski pdes |
| url | http://dx.doi.org/10.1155/S1085337503305032 |
| work_keys_str_mv | AT ilasiecka l2sregularityoftheboundarytoboundaryoperatorblforhyperbolicandpetrowskipdes AT rtriggiani l2sregularityoftheboundarytoboundaryoperatorblforhyperbolicandpetrowskipdes |