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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.
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| Colección: | Series on advances in mathematics for applied sciences ;
v. 61. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.