Linear and quasilinear parabolic problems: Volume 1 Abstract linear theory
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser
1995
|
| Schriftenreihe: | Monographs in mathematics
89 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In this treatise we present the semigroup approach to quasilinear evolution equations of parabolic type that has been developed over the last ten years, approximately. It emphasizes the dynamic viewpoint and is sufficiently general and flexible to encompass a great variety of concrete systems of partial differential equations occurring in science, some of those being of rather 'nonstandard' type. In particular, to date it is the only general method that applies to noncoercive systems. Although we are interested in nonlinear problems, our method is based on the theory of linear holomorphic semigroups. This distinguishes it from the theory of nonlinear contraction semigroups whose basis is a nonlinear version of the HilleYosida theorem: the Crandall-Liggett theorem. The latter theory is well-known and well-documented in the literature. Even though it is a powerful technique having found many applications, it is limited in its scope by the fact that, in concrete applications, it is closely tied to the maximum principle. Thus the theory of nonlinear contraction semigroups does not apply to systems, in general, since they do not allow for a maximum principle. For these reasons we do not include that theory |
| Beschreibung: | 1 Online-Ressource (XXXV, 338 Seiten) |
| ISBN: | 9783034892216 |
| DOI: | 10.1007/978-3-0348-9221-6 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-9221-6 |
| format | Electronic eBook |
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| id | DE-604.BV046059694 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:34:06Z |
| institution | BVB |
| isbn | 9783034892216 |
| language | English |
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| spelling | Amann, Herbert 1938- Verfasser (DE-588)106045687 aut Linear and quasilinear parabolic problems Volume 1 Abstract linear theory Herbert Amann Basel Birkhäuser 1995 1 Online-Ressource (XXXV, 338 Seiten) txt rdacontent c rdamedia cr rdacarrier Monographs in mathematics 89 Monographs in mathematics In this treatise we present the semigroup approach to quasilinear evolution equations of parabolic type that has been developed over the last ten years, approximately. It emphasizes the dynamic viewpoint and is sufficiently general and flexible to encompass a great variety of concrete systems of partial differential equations occurring in science, some of those being of rather 'nonstandard' type. In particular, to date it is the only general method that applies to noncoercive systems. Although we are interested in nonlinear problems, our method is based on the theory of linear holomorphic semigroups. This distinguishes it from the theory of nonlinear contraction semigroups whose basis is a nonlinear version of the HilleYosida theorem: the Crandall-Liggett theorem. The latter theory is well-known and well-documented in the literature. Even though it is a powerful technique having found many applications, it is limited in its scope by the fact that, in concrete applications, it is closely tied to the maximum principle. Thus the theory of nonlinear contraction semigroups does not apply to systems, in general, since they do not allow for a maximum principle. For these reasons we do not include that theory Mathematics Global analysis (Mathematics) Systems theory Mathematical optimization Analysis Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Mathematik (DE-604)BV046059686 1 Erscheint auch als Druck-Ausgabe 978-3-0348-9950-5 Monographs in mathematics 89 (DE-604)BV000008284 89 https://doi.org/10.1007/978-3-0348-9221-6 Verlag Volltext |
| spellingShingle | Amann, Herbert 1938- Linear and quasilinear parabolic problems Monographs in mathematics Mathematics Global analysis (Mathematics) Systems theory Mathematical optimization Analysis Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Mathematik |
| title | Linear and quasilinear parabolic problems |
| title_auth | Linear and quasilinear parabolic problems |
| title_exact_search | Linear and quasilinear parabolic problems |
| title_full | Linear and quasilinear parabolic problems Volume 1 Abstract linear theory Herbert Amann |
| title_fullStr | Linear and quasilinear parabolic problems Volume 1 Abstract linear theory Herbert Amann |
| title_full_unstemmed | Linear and quasilinear parabolic problems Volume 1 Abstract linear theory Herbert Amann |
| title_short | Linear and quasilinear parabolic problems |
| title_sort | linear and quasilinear parabolic problems abstract linear theory |
| topic | Mathematics Global analysis (Mathematics) Systems theory Mathematical optimization Analysis Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Mathematik |
| topic_facet | Mathematics Global analysis (Mathematics) Systems theory Mathematical optimization Analysis Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Mathematik |
| url | https://doi.org/10.1007/978-3-0348-9221-6 |
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| work_keys_str_mv | AT amannherbert linearandquasilinearparabolicproblemsvolume1 |