zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Asymptotic behaviour of parabolic nonautonomous evolution equations. (English) Zbl 1082.35092
Iannelli, Mimmo (ed.) et al., Functional analytic methods for evolution equations. Based on lectures given at the autumn school on evolution equations and semigroups, Levico Terme, Trento, Italy, October 28–November 2, 2001. Berlin: Springer (ISBN 3-540-23030-0/pbk). Lecture Notes in Mathematics 1855, 401-472 (2004).

The paper is concerned with the Cauchy problem for the nonautonomous evolution equation

d dtu(t)=A(t)u(t)+f(t),t>s,u(s)=x,t,sJ{[a,),},

where A(t),tJ, are linear operators on a Banach space X and xX,fC(J,X). Solutions to the problem and their properties are under consideration. A self-contained and systematic presentation of known results as well as authors’s new results are given.

The paper consists of six sections: 1. Introduction 2. Parabolic Evolution Equation 3. Exponential Dichotomy 4. Exponential Dichotomy of Parabolic Evolution Equations 5. Inhomogeneous Problems 6. Convergent Solutions for a Quasilinear Equation.

The main attention is given to the problem of exponential dichotomy and to the problem of the exponential dichotomy persistence under ‘small’ perturbations. The complete list of bibliography is represented.

MSC:
35K90Abstract parabolic equations
35B40Asymptotic behavior of solutions of PDE