Evolution equations and approximations:
This book presents an approximation theory for a general class of nonlinear evolution equations in Banach spaces and the semigroup theory, including the linear (Hille-Yosida), nonlinear (Crandall-Liggett) and time-dependent (Crandall–Pazy) theorems. The implicit finite difference method of Euler is...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Pub. Co.
c2002
|
| Schriftenreihe: | Series on advances in mathematics for applied sciences
v. 61 |
| Schlagworte: | |
| Online-Zugang: | FHN01 Volltext |
| Zusammenfassung: | This book presents an approximation theory for a general class of nonlinear evolution equations in Banach spaces and the semigroup theory, including the linear (Hille-Yosida), nonlinear (Crandall-Liggett) and time-dependent (Crandall–Pazy) theorems. The implicit finite difference method of Euler is shown to generate a sequence convergent to the unique integral solution of evolution equations of the maximal monotone type. Moreover, the Chernoff theory provides a sufficient condition for consistent and stable time integration of time-dependent nonlinear equations. The Trotter–Kato theorem and the Lie–Trotter type product formula give a mathematical framework for the convergence analysis of numerical approximations of solutions to a general class of partial differential equations. This book contains examples demonstrating the applicability of the generation as well as the approximation theory. In addition, the Kobayashi-Oharu approach of locally quasi-dissipative operators is discussed for homogeneous as well as nonhomogeneous equations. Applications to the delay differential equations, Navier–Stokes equation and scalar conservation equation are given |
| Beschreibung: | xiii, 498 p. ill |
| ISBN: | 9789812777294 |
Internformat
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| 520 | |a This book presents an approximation theory for a general class of nonlinear evolution equations in Banach spaces and the semigroup theory, including the linear (Hille-Yosida), nonlinear (Crandall-Liggett) and time-dependent (Crandall–Pazy) theorems. The implicit finite difference method of Euler is shown to generate a sequence convergent to the unique integral solution of evolution equations of the maximal monotone type. Moreover, the Chernoff theory provides a sufficient condition for consistent and stable time integration of time-dependent nonlinear equations. The Trotter–Kato theorem and the Lie–Trotter type product formula give a mathematical framework for the convergence analysis of numerical approximations of solutions to a general class of partial differential equations. This book contains examples demonstrating the applicability of the generation as well as the approximation theory. In addition, the Kobayashi-Oharu approach of locally quasi-dissipative operators is discussed for homogeneous as well as nonhomogeneous equations. Applications to the delay differential equations, Navier–Stokes equation and scalar conservation equation are given | ||
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Datensatz im Suchindex
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| author | Ito, Kazufumi |
| author_facet | Ito, Kazufumi |
| author_role | aut |
| author_sort | Ito, Kazufumi |
| author_variant | k i ki |
| building | Verbundindex |
| bvnumber | BV044635144 |
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| ctrlnum | (ZDB-124-WOP)00003798 (OCoLC)881298694 (DE-599)BVBBV044635144 |
| dewey-full | 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.353 |
| dewey-search | 515.353 |
| dewey-sort | 3515.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV044635144 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:57:46Z |
| institution | BVB |
| isbn | 9789812777294 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030033116 |
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| physical | xiii, 498 p. ill |
| psigel | ZDB-124-WOP ZDB-124-WOP FHN_PDA_WOP |
| publishDate | 2002 |
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| series2 | Series on advances in mathematics for applied sciences |
| spelling | Ito, Kazufumi Verfasser aut Evolution equations and approximations Kazufumi Ito, Franz Kappel Singapore World Scientific Pub. Co. c2002 xiii, 498 p. ill txt rdacontent c rdamedia cr rdacarrier Series on advances in mathematics for applied sciences v. 61 This book presents an approximation theory for a general class of nonlinear evolution equations in Banach spaces and the semigroup theory, including the linear (Hille-Yosida), nonlinear (Crandall-Liggett) and time-dependent (Crandall–Pazy) theorems. The implicit finite difference method of Euler is shown to generate a sequence convergent to the unique integral solution of evolution equations of the maximal monotone type. Moreover, the Chernoff theory provides a sufficient condition for consistent and stable time integration of time-dependent nonlinear equations. The Trotter–Kato theorem and the Lie–Trotter type product formula give a mathematical framework for the convergence analysis of numerical approximations of solutions to a general class of partial differential equations. This book contains examples demonstrating the applicability of the generation as well as the approximation theory. In addition, the Kobayashi-Oharu approach of locally quasi-dissipative operators is discussed for homogeneous as well as nonhomogeneous equations. Applications to the delay differential equations, Navier–Stokes equation and scalar conservation equation are given Evolution equations / Numerical solutions Approximation theory Evolutionsgleichung (DE-588)4129061-6 gnd rswk-swf Approximationstheorie (DE-588)4120913-8 gnd rswk-swf Evolutionsgleichung (DE-588)4129061-6 s 1\p DE-604 Approximationstheorie (DE-588)4120913-8 s 2\p DE-604 Kappel, F. Sonstige oth Erscheint auch als Druck-Ausgabe 9789812380265 Erscheint auch als Druck-Ausgabe 9812380264 http://www.worldscientific.com/worldscibooks/10.1142/4990#t=toc Verlag URL des Erstveroeffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ito, Kazufumi Evolution equations and approximations Evolution equations / Numerical solutions Approximation theory Evolutionsgleichung (DE-588)4129061-6 gnd Approximationstheorie (DE-588)4120913-8 gnd |
| subject_GND | (DE-588)4129061-6 (DE-588)4120913-8 |
| title | Evolution equations and approximations |
| title_auth | Evolution equations and approximations |
| title_exact_search | Evolution equations and approximations |
| title_full | Evolution equations and approximations Kazufumi Ito, Franz Kappel |
| title_fullStr | Evolution equations and approximations Kazufumi Ito, Franz Kappel |
| title_full_unstemmed | Evolution equations and approximations Kazufumi Ito, Franz Kappel |
| title_short | Evolution equations and approximations |
| title_sort | evolution equations and approximations |
| topic | Evolution equations / Numerical solutions Approximation theory Evolutionsgleichung (DE-588)4129061-6 gnd Approximationstheorie (DE-588)4120913-8 gnd |
| topic_facet | Evolution equations / Numerical solutions Approximation theory Evolutionsgleichung Approximationstheorie |
| url | http://www.worldscientific.com/worldscibooks/10.1142/4990#t=toc |
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