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
- Rights
- restrictedAccess
- License
- http://creativecommons.org/licenses/by-nc-nd/4.0/
| Summary: | 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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