Evolution equations and approximations /:
Annotation Ito (North Carolina State U.) and Kappel (U. of Graz, Austria) offer a unified presentation of the general approach for well-posedness results using abstract evolution equations, drawing from and modifying the work of K. and Y. Kobayashi and S. Oharu. They also explore abstract approximat...
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| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
River Edge, N.J. :
World Scientific,
©2002.
|
| Series: | Series on advances in mathematics for applied sciences ;
v. 61. |
| Subjects: | |
| Online Access: | DE-862 DE-863 |
| Summary: | Annotation Ito (North Carolina State U.) and Kappel (U. of Graz, Austria) offer a unified presentation of the general approach for well-posedness results using abstract evolution equations, drawing from and modifying the work of K. and Y. Kobayashi and S. Oharu. They also explore abstract approximation results for evolution equations. Their work is not a textbook, but they explain how instructors can use various sections, or combinations of them, as a foundation for a range of courses. Annotation copyrighted by Book News, Inc., Portland, OR. |
| Physical Description: | 1 online resource (xiii, 498 pages) : illustrations |
| Bibliography: | Includes bibliographical references (pages 489-492) and index. |
| ISBN: | 9789812777294 9812777296 9789812380265 9812380264 |
Staff View
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| 245 | 1 | 0 | |a Evolution equations and approximations / |c Kazufumi Ito, Franz Kappel. |
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| 300 | |a 1 online resource (xiii, 498 pages) : |b illustrations | ||
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| 490 | 1 | |a Series on advances in mathematics for applied sciences ; |v v. 61 | |
| 504 | |a Includes bibliographical references (pages 489-492) and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | 8 | |a Annotation Ito (North Carolina State U.) and Kappel (U. of Graz, Austria) offer a unified presentation of the general approach for well-posedness results using abstract evolution equations, drawing from and modifying the work of K. and Y. Kobayashi and S. Oharu. They also explore abstract approximation results for evolution equations. Their work is not a textbook, but they explain how instructors can use various sections, or combinations of them, as a foundation for a range of courses. Annotation copyrighted by Book News, Inc., Portland, OR. | |
| 505 | 0 | |a Ch. 1. Dissipative and maximal monotone operators. 1.1. Duality mapping and directional derivatives of norms. 1.2. Dissipative operators. 1.3. Properties of m-dissipative operators. 1.4. Perturbation results for m-dissipative operators. 1.5. Maximal monotone operators. 1.6. Convex functionals and subdifferentials -- ch. 2. Linear semigroups. 2.1. Examples and basic definitions. 2.2. Cauchy problems and mild solutions. 2.3. The Hille-Yosida theorem. 2.4. The Lumer-Phillips theorem. 2.5. A second order equation -- ch. 3. Analytic semigroups. 3.1. Dissipative operators and sesquilinear forms. 3.2. Analytic semigroups -- ch. 4. Approximation of C[symbol]-semigroups. 4.1. The Trotter-Kato theorem. 4.2. Approximation of nonhomogeneous problems. 4.3. Variational formulations of the Trotter-Kato theorem. 4.4. An approximation result for analytic semigroups -- ch. 5. Nonlinear semigroups of contractions. 5.1. Generation of nonlinear semigroups. 5.2. Cauchy problems with dissipative operators. 5.3. The infinitesimal generator. 5.4. Nonlinear diffusion -- ch. 6. Locally quasi-dissipative evolution equations. 6.1. Locally quasi-dissipative operators. 6.2. Assumptions on the operators A(t). 6.3. DS-approximations and fundamental estimates. 6.4. Existence of DS-approximations. 6.5. Existence and uniqueness of mild solutions. 6.6. Autonomous problems. 6.7. "Nonhomogeneous" problems. 6.8. Strong solutions. 6.9. Quasi-linear equations. 6.10. A "parabolic" problem -- ch. 7. The Crandall-Pazy class. 7.1. The conditions. 7.2. Existence of an evolution operator -- ch. 8. Variational formulations and Gelfand triples. 8.1. Cauchy problems and Gelfand triples. 8.2. An approximation result -- ch. 9. Applications to concrete systems. 9.1. Delay-differential equations. 9.2. Scalar conservation laws. 9.3. The Navier-Stokes equations -- ch. 10. Approximation of solutions for evolution equations. 10.1. Approximation by approximating evolution problems. 10.2. Chernoff's theorem. 10.3. Operator splitt -- ch. 11. Semilinear evolution equations. 11.1. Well-posedness. 11.2. Delay equations with time and state dependent delays. 11.3. Approximation theory. 11.4. A concrete approximation scheme for delay systems. | |
| 650 | 0 | |a Evolution equations |x Numerical solutions. |0 http://id.loc.gov/authorities/subjects/sh85046036 | |
| 650 | 0 | |a Approximation theory. |0 http://id.loc.gov/authorities/subjects/sh85006190 | |
| 650 | 6 | |a Équations d'évolution |x Solutions numériques. | |
| 650 | 6 | |a Théorie de l'approximation. | |
| 650 | 7 | |a MATHEMATICS |x Differential Equations |x Partial. |2 bisacsh | |
| 650 | 7 | |a Approximation theory |2 fast | |
| 650 | 7 | |a Evolution equations |x Numerical solutions |2 fast | |
| 655 | 0 | |a Electronic books. | |
| 700 | 1 | |a Kappel, F. | |
| 758 | |i has work: |a Evolution equations and approximations (Text) |1 https://id.oclc.org/worldcat/entity/E39PCG7fD3F4yGGhQHhTFYFVG3 |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
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| contents | Ch. 1. Dissipative and maximal monotone operators. 1.1. Duality mapping and directional derivatives of norms. 1.2. Dissipative operators. 1.3. Properties of m-dissipative operators. 1.4. Perturbation results for m-dissipative operators. 1.5. Maximal monotone operators. 1.6. Convex functionals and subdifferentials -- ch. 2. Linear semigroups. 2.1. Examples and basic definitions. 2.2. Cauchy problems and mild solutions. 2.3. The Hille-Yosida theorem. 2.4. The Lumer-Phillips theorem. 2.5. A second order equation -- ch. 3. Analytic semigroups. 3.1. Dissipative operators and sesquilinear forms. 3.2. Analytic semigroups -- ch. 4. Approximation of C[symbol]-semigroups. 4.1. The Trotter-Kato theorem. 4.2. Approximation of nonhomogeneous problems. 4.3. Variational formulations of the Trotter-Kato theorem. 4.4. An approximation result for analytic semigroups -- ch. 5. Nonlinear semigroups of contractions. 5.1. Generation of nonlinear semigroups. 5.2. Cauchy problems with dissipative operators. 5.3. The infinitesimal generator. 5.4. Nonlinear diffusion -- ch. 6. Locally quasi-dissipative evolution equations. 6.1. Locally quasi-dissipative operators. 6.2. Assumptions on the operators A(t). 6.3. DS-approximations and fundamental estimates. 6.4. Existence of DS-approximations. 6.5. Existence and uniqueness of mild solutions. 6.6. Autonomous problems. 6.7. "Nonhomogeneous" problems. 6.8. Strong solutions. 6.9. Quasi-linear equations. 6.10. A "parabolic" problem -- ch. 7. The Crandall-Pazy class. 7.1. The conditions. 7.2. Existence of an evolution operator -- ch. 8. Variational formulations and Gelfand triples. 8.1. Cauchy problems and Gelfand triples. 8.2. An approximation result -- ch. 9. Applications to concrete systems. 9.1. Delay-differential equations. 9.2. Scalar conservation laws. 9.3. The Navier-Stokes equations -- ch. 10. Approximation of solutions for evolution equations. 10.1. Approximation by approximating evolution problems. 10.2. Chernoff's theorem. 10.3. Operator splitt -- ch. 11. Semilinear evolution equations. 11.1. Well-posedness. 11.2. Delay equations with time and state dependent delays. 11.3. Approximation theory. 11.4. A concrete approximation scheme for delay systems. |
| ctrlnum | (OCoLC)614463806 |
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| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
| format | Electronic eBook |
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ind1="1" ind2=" "><subfield code="a">Series on advances in mathematics for applied sciences ;</subfield><subfield code="v">v. 61</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (pages 489-492) and index.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="520" ind1="8" ind2=" "><subfield code="a">Annotation Ito (North Carolina State U.) and Kappel (U. of Graz, Austria) offer a unified presentation of the general approach for well-posedness results using abstract evolution equations, drawing from and modifying the work of K. and Y. Kobayashi and S. Oharu. They also explore abstract approximation results for evolution equations. Their work is not a textbook, but they explain how instructors can use various sections, or combinations of them, as a foundation for a range of courses. Annotation copyrighted by Book News, Inc., Portland, OR.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Ch. 1. Dissipative and maximal monotone operators. 1.1. Duality mapping and directional derivatives of norms. 1.2. Dissipative operators. 1.3. Properties of m-dissipative operators. 1.4. Perturbation results for m-dissipative operators. 1.5. Maximal monotone operators. 1.6. Convex functionals and subdifferentials -- ch. 2. Linear semigroups. 2.1. Examples and basic definitions. 2.2. Cauchy problems and mild solutions. 2.3. The Hille-Yosida theorem. 2.4. The Lumer-Phillips theorem. 2.5. A second order equation -- ch. 3. Analytic semigroups. 3.1. Dissipative operators and sesquilinear forms. 3.2. Analytic semigroups -- ch. 4. Approximation of C[symbol]-semigroups. 4.1. The Trotter-Kato theorem. 4.2. Approximation of nonhomogeneous problems. 4.3. Variational formulations of the Trotter-Kato theorem. 4.4. An approximation result for analytic semigroups -- ch. 5. Nonlinear semigroups of contractions. 5.1. Generation of nonlinear semigroups. 5.2. Cauchy problems with dissipative operators. 5.3. The infinitesimal generator. 5.4. Nonlinear diffusion -- ch. 6. Locally quasi-dissipative evolution equations. 6.1. Locally quasi-dissipative operators. 6.2. Assumptions on the operators A(t). 6.3. DS-approximations and fundamental estimates. 6.4. Existence of DS-approximations. 6.5. Existence and uniqueness of mild solutions. 6.6. Autonomous problems. 6.7. "Nonhomogeneous" problems. 6.8. Strong solutions. 6.9. Quasi-linear equations. 6.10. A "parabolic" problem -- ch. 7. The Crandall-Pazy class. 7.1. The conditions. 7.2. Existence of an evolution operator -- ch. 8. Variational formulations and Gelfand triples. 8.1. Cauchy problems and Gelfand triples. 8.2. An approximation result -- ch. 9. Applications to concrete systems. 9.1. Delay-differential equations. 9.2. Scalar conservation laws. 9.3. The Navier-Stokes equations -- ch. 10. Approximation of solutions for evolution equations. 10.1. Approximation by approximating evolution problems. 10.2. Chernoff's theorem. 10.3. Operator splitt -- ch. 11. Semilinear evolution equations. 11.1. Well-posedness. 11.2. Delay equations with time and state dependent delays. 11.3. Approximation theory. 11.4. 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| genre | Electronic books. |
| genre_facet | Electronic books. |
| id | ZDB-4-EBA-ocn614463806 |
| illustrated | Illustrated |
| indexdate | 2025-04-11T08:36:43Z |
| institution | BVB |
| isbn | 9789812777294 9812777296 9789812380265 9812380264 |
| language | English |
| oclc_num | 614463806 |
| open_access_boolean | |
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| physical | 1 online resource (xiii, 498 pages) : illustrations |
| psigel | ZDB-4-EBA FWS_PDA_EBA ZDB-4-EBA |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | World Scientific, |
| record_format | marc |
| series | Series on advances in mathematics for applied sciences ; |
| series2 | Series on advances in mathematics for applied sciences ; |
| spelling | Ito, Kazufumi. Evolution equations and approximations / Kazufumi Ito, Franz Kappel. River Edge, N.J. : World Scientific, ©2002. 1 online resource (xiii, 498 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Series on advances in mathematics for applied sciences ; v. 61 Includes bibliographical references (pages 489-492) and index. Print version record. Annotation Ito (North Carolina State U.) and Kappel (U. of Graz, Austria) offer a unified presentation of the general approach for well-posedness results using abstract evolution equations, drawing from and modifying the work of K. and Y. Kobayashi and S. Oharu. They also explore abstract approximation results for evolution equations. Their work is not a textbook, but they explain how instructors can use various sections, or combinations of them, as a foundation for a range of courses. Annotation copyrighted by Book News, Inc., Portland, OR. Ch. 1. Dissipative and maximal monotone operators. 1.1. Duality mapping and directional derivatives of norms. 1.2. Dissipative operators. 1.3. Properties of m-dissipative operators. 1.4. Perturbation results for m-dissipative operators. 1.5. Maximal monotone operators. 1.6. Convex functionals and subdifferentials -- ch. 2. Linear semigroups. 2.1. Examples and basic definitions. 2.2. Cauchy problems and mild solutions. 2.3. The Hille-Yosida theorem. 2.4. The Lumer-Phillips theorem. 2.5. A second order equation -- ch. 3. Analytic semigroups. 3.1. Dissipative operators and sesquilinear forms. 3.2. Analytic semigroups -- ch. 4. Approximation of C[symbol]-semigroups. 4.1. The Trotter-Kato theorem. 4.2. Approximation of nonhomogeneous problems. 4.3. Variational formulations of the Trotter-Kato theorem. 4.4. An approximation result for analytic semigroups -- ch. 5. Nonlinear semigroups of contractions. 5.1. Generation of nonlinear semigroups. 5.2. Cauchy problems with dissipative operators. 5.3. The infinitesimal generator. 5.4. Nonlinear diffusion -- ch. 6. Locally quasi-dissipative evolution equations. 6.1. Locally quasi-dissipative operators. 6.2. Assumptions on the operators A(t). 6.3. DS-approximations and fundamental estimates. 6.4. Existence of DS-approximations. 6.5. Existence and uniqueness of mild solutions. 6.6. Autonomous problems. 6.7. "Nonhomogeneous" problems. 6.8. Strong solutions. 6.9. Quasi-linear equations. 6.10. A "parabolic" problem -- ch. 7. The Crandall-Pazy class. 7.1. The conditions. 7.2. Existence of an evolution operator -- ch. 8. Variational formulations and Gelfand triples. 8.1. Cauchy problems and Gelfand triples. 8.2. An approximation result -- ch. 9. Applications to concrete systems. 9.1. Delay-differential equations. 9.2. Scalar conservation laws. 9.3. The Navier-Stokes equations -- ch. 10. Approximation of solutions for evolution equations. 10.1. Approximation by approximating evolution problems. 10.2. Chernoff's theorem. 10.3. Operator splitt -- ch. 11. Semilinear evolution equations. 11.1. Well-posedness. 11.2. Delay equations with time and state dependent delays. 11.3. Approximation theory. 11.4. A concrete approximation scheme for delay systems. Evolution equations Numerical solutions. http://id.loc.gov/authorities/subjects/sh85046036 Approximation theory. http://id.loc.gov/authorities/subjects/sh85006190 Équations d'évolution Solutions numériques. Théorie de l'approximation. MATHEMATICS Differential Equations Partial. bisacsh Approximation theory fast Evolution equations Numerical solutions fast Electronic books. Kappel, F. has work: Evolution equations and approximations (Text) https://id.oclc.org/worldcat/entity/E39PCG7fD3F4yGGhQHhTFYFVG3 https://id.oclc.org/worldcat/ontology/hasWork Print version: Ito, Kazufumi. Evolution equations and approximations. River Edge, N.J. : World Scientific, ©2002 9812380264 9789812380265 (DLC) 2002072092 (OCoLC)49936144 Series on advances in mathematics for applied sciences ; v. 61. http://id.loc.gov/authorities/names/n90710999 |
| spellingShingle | Ito, Kazufumi Evolution equations and approximations / Series on advances in mathematics for applied sciences ; Ch. 1. Dissipative and maximal monotone operators. 1.1. Duality mapping and directional derivatives of norms. 1.2. Dissipative operators. 1.3. Properties of m-dissipative operators. 1.4. Perturbation results for m-dissipative operators. 1.5. Maximal monotone operators. 1.6. Convex functionals and subdifferentials -- ch. 2. Linear semigroups. 2.1. Examples and basic definitions. 2.2. Cauchy problems and mild solutions. 2.3. The Hille-Yosida theorem. 2.4. The Lumer-Phillips theorem. 2.5. A second order equation -- ch. 3. Analytic semigroups. 3.1. Dissipative operators and sesquilinear forms. 3.2. Analytic semigroups -- ch. 4. Approximation of C[symbol]-semigroups. 4.1. The Trotter-Kato theorem. 4.2. Approximation of nonhomogeneous problems. 4.3. Variational formulations of the Trotter-Kato theorem. 4.4. An approximation result for analytic semigroups -- ch. 5. Nonlinear semigroups of contractions. 5.1. Generation of nonlinear semigroups. 5.2. Cauchy problems with dissipative operators. 5.3. The infinitesimal generator. 5.4. Nonlinear diffusion -- ch. 6. Locally quasi-dissipative evolution equations. 6.1. Locally quasi-dissipative operators. 6.2. Assumptions on the operators A(t). 6.3. DS-approximations and fundamental estimates. 6.4. Existence of DS-approximations. 6.5. Existence and uniqueness of mild solutions. 6.6. Autonomous problems. 6.7. "Nonhomogeneous" problems. 6.8. Strong solutions. 6.9. Quasi-linear equations. 6.10. A "parabolic" problem -- ch. 7. The Crandall-Pazy class. 7.1. The conditions. 7.2. Existence of an evolution operator -- ch. 8. Variational formulations and Gelfand triples. 8.1. Cauchy problems and Gelfand triples. 8.2. An approximation result -- ch. 9. Applications to concrete systems. 9.1. Delay-differential equations. 9.2. Scalar conservation laws. 9.3. The Navier-Stokes equations -- ch. 10. Approximation of solutions for evolution equations. 10.1. Approximation by approximating evolution problems. 10.2. Chernoff's theorem. 10.3. Operator splitt -- ch. 11. Semilinear evolution equations. 11.1. Well-posedness. 11.2. Delay equations with time and state dependent delays. 11.3. Approximation theory. 11.4. A concrete approximation scheme for delay systems. Evolution equations Numerical solutions. http://id.loc.gov/authorities/subjects/sh85046036 Approximation theory. http://id.loc.gov/authorities/subjects/sh85006190 Équations d'évolution Solutions numériques. Théorie de l'approximation. MATHEMATICS Differential Equations Partial. bisacsh Approximation theory fast Evolution equations Numerical solutions fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85046036 http://id.loc.gov/authorities/subjects/sh85006190 |
| 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. http://id.loc.gov/authorities/subjects/sh85046036 Approximation theory. http://id.loc.gov/authorities/subjects/sh85006190 Équations d'évolution Solutions numériques. Théorie de l'approximation. MATHEMATICS Differential Equations Partial. bisacsh Approximation theory fast Evolution equations Numerical solutions fast |
| topic_facet | Evolution equations Numerical solutions. Approximation theory. Équations d'évolution Solutions numériques. Théorie de l'approximation. MATHEMATICS Differential Equations Partial. Approximation theory Evolution equations Numerical solutions Electronic books. |
| work_keys_str_mv | AT itokazufumi evolutionequationsandapproximations AT kappelf evolutionequationsandapproximations |