Existence Families, Functional Calculi and Evolution Equations
This book presents an operator-theoretic approach to ill-posed evolution equations. It presents the basic theory, and the more surprising examples, of generalizations of strongly continuous semigroups known as 'existent families' and 'regularized semigroups'. These families of op...
Guardat en:
| Autor principal: | |
|---|---|
| Format: | Livre numérique |
| Idioma: | Anglais |
| Publicat: |
Berlin [etc.] :
Springer
[20..].
Cham : Springer Nature |
| Col·lecció: | Lecture notes in mathematics
1570 |
| Matèries: | |
| Accés en línia: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Existence families, functional calculi and evolution equations, Ralph deLaubenfels, 1994, Berlin, Springer-Verlag, 1 volume (XV-234 pages), Lecture notes in mathematics, 3-540-57703-3 • Existence Families, Functional Calculi and Evolution Equations, Texte imprimé, 9783662188910 |
Taula de continguts:
- Intuition and elementary examples
- Existence families
- Regularized semigroups
- The solution space of an operator and automatic well-posedness
- Exponentially bounded (Banach) solution spaces
- Well-posedness on a larger space; Generalized solutions
- Entire vectors and entire existence families
- Reversibility of parabolic problems
- The cauchy problem for the Laplace equation
- Boundary values of holomorphic semigroups
- The Schrödinger equation
- Functional calculus for commuting generators of bounded strongly continuous groups
- Petrovsky correct matrices of generators of bounded strongly continuous groups
- Arbitrary matrices of generators of bounded strongly continuous groups
- More examples of regularized semigroups
- Existence and uniqueness families
- C-resolvents and Hille-Yosida type theorems
- Relationship to integrated semigroups
- Perturbations
- Type of an operator
- Holomorphic C-existence families
- Unbounded holomorphic functional calculus for operators with polynomially bounded resolvents
- Spectral conditions guaranteeing solutions of the abstract Cauchy problem
- Polynomials of generators
- Iterated abstract Cauchy problems
- Equipartition of energy
- Simultaneous solution space
- Exponentially bounded simultaneous solution space
- Simultaneous existence families
- Simultaneous existence families for matrices of operators
- Time dependent evolution equations.