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)
Random attractor for a damped sine-Gordon equation with white noise. (English) Zbl 1065.37057

It is shown that a sine-Gordon equation with additive white noise, formally given by

u tt +αu t -Δu+βsinu=qW ˙

on an open bounded Ω n with smooth boundary, where α>0, qH 2 (Ω)H 0 1 (Ω), W ˙ is the formal derivative of a one-dimensional Wiener process, imposing Dirichlet conditions, has a random attractor. A nonrandom upper bound for the Hausdorff dimension of the random attractor, which decreases as the damping α grows, is derived. The Hausdorff dimension of random attractors has been shown to be nonrandom almost surely by H. Crauel and F. Flandoli [J. Dyn. Differ. Equations 10, 449-474 (1998; Zbl 0927.37031)].

MSC:
37L30Attractors and their dimensions, Lyapunov exponents
35R60PDEs with randomness, stochastic PDE
35B41Attractors (PDE)
35Q53KdV-like (Korteweg-de Vries) equations
37L55Infinite-dimensional random dynamical systems; stochastic equations
60H15Stochastic partial differential equations