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)
Almost periodicity of inhomogeneous parabolic evolution equations. (English) Zbl 1047.35078
Ruiz Goldstein, Gisèle (ed.) et al., Evolution equations. Proceedings of the conference, Blaubeuren, Germany, June 11–17, 2001 in honor of the 60th birthdays of Philippe Bénilan, Jerome A. Goldstein and Rainer Nagel. New York, NY: Marcel Dekker (ISBN 0-8247-0975-6/pbk). Lect. Notes Pure Appl. Math. 234, 299-318 (2003).

The authors deal with the problem of almost periodicity of solutions of the (parabolic) differential equation

${u}^{\text{'}}\left(t\right)=A\left(t\right)u\left(t\right)+f\left(t\right),\phantom{\rule{2.em}{0ex}}\left(\mathrm{E}\right)$

on $ℝ$ or on ${ℝ}_{+}$. In the second case an initial condition of the form $u\left(0\right)=x\in X=$ the underlying Banach space. Relying on such concepts like evolution family of bounded operators (on $X$), Yosida approximation, they prove existence of almost periodic solutions for the equation (E) on the real line $ℝ$, and the existence of asymptotically almost periodic solutions for the equation (E) on the half-line ${ℝ}_{+}$. Conditions are formulated assuring exponential asymptotic stability for the corresponding homogeneous equation.

MSC:
 35K90 Abstract parabolic equations 34G10 Linear ODE in abstract spaces 34C27 Almost and pseudo-almost periodic solutions of ODE