Research Catalog

Title

Evolution equations and approximations / Kazufumi Ito, Franz Kappel.

Author

Ito, Kazufumi.

Publication

River Edge, N.J. : World Scientific, [2002], ©2002.

Items in the Library & Off-site

Holdings

Details

Additional Authors

Kappel, F.

Description

xiii, 498 pages : illustrations; 23 cm.

Series Statement

Series on advances in mathematics for applied sciences ; v. 61

Uniform Title

Series on advances in mathematics for applied sciences ; v. 61.

Subject

• Evolution equations > Numerical solutions
• Approximation theory

Bibliography (note)

• Includes bibliographical references (p. 489-492) and index.

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[subscript 0]-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 splitting -- 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. App. A.1. Some inequalities -- App. A.2. Convergence of Steklov means -- App. A.3. Some technical results needed in Section 9.2.

ISBN

9812380264 (alk. paper)

LCCN

2002072092

OCLC

• ocm49936144
• SCSB-4302549

Owning Institutions

Columbia University Libraries