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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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
River Edge, N.J. :
World Scientific,
©2002.
|
| Colección: | Series on advances in mathematics for applied sciences ;
v. 61. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Ito, Kazufumi. | |
| 245 | 1 | 0 | |a Evolution equations and approximations / |c Kazufumi Ito, Franz Kappel. |
| 260 | |a River Edge, N.J. : |b World Scientific, |c ©2002. | ||
| 300 | |a 1 online resource (xiii, 498 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 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. | |
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Evolution equations |x Numerical solutions. | |
| 650 | 0 | |a Approximation theory. | |
| 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 | |
| 700 | 1 | |a Kappel, F. | |
| 776 | 0 | 8 | |i Print version: |a Ito, Kazufumi. |t Evolution equations and approximations. |d River Edge, N.J. : World Scientific, ©2002 |z 9812380264 |z 9789812380265 |w (DLC) 2002072092 |w (OCoLC)49936144 |
| 830 | 0 | |a Series on advances in mathematics for applied sciences ; |v v. 61. | |
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