Global attractors in abstract parabolic problems /

This book investigates the asymptotic behaviour of dynamical systems corresponding to parabolic equations.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Cholewa, Jan W.
Autor Corporativo: London Mathematical Society
Otros Autores: Dlotko, Tomasz
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge, UK ; New York : Cambridge University Press, 2000.
Colección:London Mathematical Society lecture note series ; 278.
Temas:
Attractors (Mathematics)
Differential equations, Parabolic.
Attracteurs (Mathématiques)
Équations différentielles paraboliques.
MATHEMATICS > Topology.
Parabolische differentiaalvergelijkingen.
Dynamische systemen.
Equations différentielles paraboliques.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Ch. 1. Preliminary Concepts
  • 1.1. Elements of stability theory
  • 1.2. Inequalities. Elliptic operators
  • 1.3. Sectorial operators
  • Ch. 2. The abstract Cauchy problem
  • 2.1. Evolutionary equation with sectorial operator
  • 2.2. Variation of constants formula
  • 2.3. Local X[superscript [alpha]] solutions
  • Ch. 3. Semigroups of global solutions
  • 3.1. Generation of nonlinear semigroups
  • 3.2. Smoothing properties of the semigroup
  • 3.3. Compactness results
  • Ch. 4. Construction of the global attractor
  • 4.1. Dissipativeness of {T(t)}
  • 4.2. Existence of a global attractor
  • abstract setting
  • 4.3. Global solvability and attractors in X[superscript [alpha]] scales
  • Ch. 5. Application of abstract results to parabolic equations
  • 5.1. Formulation of the problem
  • 5.2. Global solutions via partial information
  • 5.3. Existence of a global attractor
  • Ch. 6. Examples of global attractors in parabolic problems
  • 6.1. Introductory example
  • 6.2. Single second order dissipative equation
  • 6.3. The method of invariant regions
  • 6.4. The Cahn-Hilliard pattern formation model
  • 6.5. Burgers equation
  • 6.6. Navier-Stokes equations in low dimension (n [less than or equal to] 2)
  • 6.7. Cauchy problems in the half-space R[superscript +] x R[superscript n]
  • Ch. 7. Backward uniqueness and regularity of solutions
  • 7.1. Invertible processes
  • 7.2. X[superscript s+[alpha]] solutions; s [greater than or equal to] 0, [alpha][Epsilon](0,1)
  • Ch. 8. Extensions
  • 8.1. Non-Lipschitz nonlinearities
  • 8.2. Application of the principle of linearized stability
  • 8.3. The n-dimensional Navier-Stokes system
  • 8.4. Parabolic problems in Holder spaces
  • 8.5. Dissipativeness in Holder spaces
  • 8.6. Equations with monotone operators
  • Ch. 9. Appendix
  • 9.1. Notation, definitions and conventions
  • 9.2. Abstract version of the maximum principle
  • 9.3. L[superscript [infinity]]([Omega]) estimate for second order problems
  • 9.4. Comparison of X[superscript [alpha]] solution with other types of solutions
  • 9.5. Final remarks.

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