Perturbing the boundary conditions of the generator of a cosine family
Let A be a densely defined, closed linear operator (which we shall call maximal operator) with domain D(A) on a Banach space X and consider closed linear operators L:D(A)→∂X and Φ:D(A)→∂X (where ∂X is another Banach space called boundary space). Putting conditions on L and Φ, we show that the second...
- Autores:
- Tipo de recurso:
- Fecha de publicación:
- 2012
- Institución:
- Universidad Tecnológica de Bolívar
- Repositorio:
- Repositorio Institucional UTB
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.utb.edu.co:20.500.12585/9097
- Acceso en línea:
- https://hdl.handle.net/20.500.12585/9097
- Palabra clave:
- Abstract Cauchy problems
Analytic C 0-semigroups
Cosine functions
General boundary conditions
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- restrictedAccess
- License
- http://creativecommons.org/licenses/by-nc-nd/4.0/
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2020-03-26T16:32:56Z2020-03-26T16:32:56Z2012Semigroup Forum; Vol. 85, Núm. 1; pp. 58-7400371912https://hdl.handle.net/20.500.12585/909710.1007/s00233-011-9361-3Universidad Tecnológica de BolívarRepositorio UTB56501378100Let A be a densely defined, closed linear operator (which we shall call maximal operator) with domain D(A) on a Banach space X and consider closed linear operators L:D(A)→∂X and Φ:D(A)→∂X (where ∂X is another Banach space called boundary space). Putting conditions on L and Φ, we show that the second order abstract Cauchy problem for the operator A Φ with A Φu=Au and domain D(A Φ):={u∈D(A):Lu=Φu} is well-posed and thus it generates a cosine operator function on the Banach space X. © 2011 Springer Science+Business Media, LLC.Recurso electrónicoapplication/pdfenghttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/restrictedAccessAtribución-NoComercial 4.0 Internacionalhttp://purl.org/coar/access_right/c_16echttps://www.scopus.com/inward/record.uri?eid=2-s2.0-84864395196&doi=10.1007%2fs00233-011-9361-3&partnerID=40&md5=261384bcd6c5814b2a915f1802e0d008Perturbing the boundary conditions of the generator of a cosine familyinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_2df8fbb1Abstract Cauchy problemsAnalytic C 0-semigroupsCosine functionsGeneral boundary conditionsAlvarez-Pardo, E.Arendt, W., Batty, C., Hieber, M., Neubrander, F., (2001) Vector-Valued Laplace Transforms and Cauchy Problems, , Basel: BirkhäuserBátkai, A., Engel, K.-J., Abstract wave equations with generalized Wentzell boundary conditions (2004) J. Differ. Equ., 207, pp. 1-20Chill, R., Keyantuo, V., Warma, M., Generation a cosine families on L p(0,1) by elliptic operators with Robin boundary conditions (2007) Functional Analysis and Evolutions Equations, Günter Lumer Volume, pp. 113-130Goldstein, J., (1985) Semigroups of Linear Operators and Applications, , New York: Oxford University PressGreiner, G., Perturbing the boundary conditions of a generator (1987) Houst. J. Math., 13, pp. 213-229Greiner, G., Kuhn, K., Linear and semilinear boundary conditions: the analytic case (1991) Lecture Notes in Pure and Applied Mathematics, 135, pp. 193-211Hoppe, R., Interpolation of cosine operator functions (1984) Ann. Mat. Pura Appl., 136, pp. 183-212Keyantuo, V., Warma, M., The wave equation on L p spaces (2005) Semigroup Forum, 71, pp. 73-92Keyantuo, V., Warma, M., The wave equation with Wentzell-Robin boundary conditions on L p spaces (2006) J. Differ. Equ., 229, pp. 680-697Kisyński, J., On cosine operator functions and one-parameter groups operators (1969) Stud. Math., 44, pp. 93-105Mugnolo, D., Operator matrices as generators of cosine operator functions (2006) Integral Equ. Oper. Theory, 54, pp. 441-464Nickel, G., A new look at boundary perturbations of generators (2004) Electron. J. Differ. Equ., 95, pp. 1-14Piskarev, S., Shaw, S.-Y., Perturbation and comparison of cosine operator functions (1995) Semigroup Forum, 51, pp. 225-246Xiao, T.-J., Liang, J., Second order differential operators with Feller-Wentzell type boundary conditions (2008) J. Funct. Anal., 254, pp. 1467-1486http://purl.org/coar/resource_type/c_6501THUMBNAILMiniProdInv.pngMiniProdInv.pngimage/png23941https://repositorio.utb.edu.co/bitstream/20.500.12585/9097/1/MiniProdInv.png0cb0f101a8d16897fb46fc914d3d7043MD5120.500.12585/9097oai:repositorio.utb.edu.co:20.500.12585/90972023-05-25 10:24:18.913Repositorio Institucional UTBrepositorioutb@utb.edu.co |
| dc.title.none.fl_str_mv |
Perturbing the boundary conditions of the generator of a cosine family |
| title |
Perturbing the boundary conditions of the generator of a cosine family |
| spellingShingle |
Perturbing the boundary conditions of the generator of a cosine family Abstract Cauchy problems Analytic C 0-semigroups Cosine functions General boundary conditions |
| title_short |
Perturbing the boundary conditions of the generator of a cosine family |
| title_full |
Perturbing the boundary conditions of the generator of a cosine family |
| title_fullStr |
Perturbing the boundary conditions of the generator of a cosine family |
| title_full_unstemmed |
Perturbing the boundary conditions of the generator of a cosine family |
| title_sort |
Perturbing the boundary conditions of the generator of a cosine family |
| dc.subject.keywords.none.fl_str_mv |
Abstract Cauchy problems Analytic C 0-semigroups Cosine functions General boundary conditions |
| topic |
Abstract Cauchy problems Analytic C 0-semigroups Cosine functions General boundary conditions |
| description |
Let A be a densely defined, closed linear operator (which we shall call maximal operator) with domain D(A) on a Banach space X and consider closed linear operators L:D(A)→∂X and Φ:D(A)→∂X (where ∂X is another Banach space called boundary space). Putting conditions on L and Φ, we show that the second order abstract Cauchy problem for the operator A Φ with A Φu=Au and domain D(A Φ):={u∈D(A):Lu=Φu} is well-posed and thus it generates a cosine operator function on the Banach space X. © 2011 Springer Science+Business Media, LLC. |
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2012 |
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2012 |
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2020-03-26T16:32:56Z |
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2020-03-26T16:32:56Z |
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Artículo |
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publishedVersion |
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Semigroup Forum; Vol. 85, Núm. 1; pp. 58-74 |
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00371912 |
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https://hdl.handle.net/20.500.12585/9097 |
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10.1007/s00233-011-9361-3 |
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Universidad Tecnológica de Bolívar |
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Repositorio UTB |
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56501378100 |
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Semigroup Forum; Vol. 85, Núm. 1; pp. 58-74 00371912 10.1007/s00233-011-9361-3 Universidad Tecnológica de Bolívar Repositorio UTB 56501378100 |
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https://hdl.handle.net/20.500.12585/9097 |
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eng |
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