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)
Upper semicontinuity of attractors for lattice systems under singular perturbations. (English) Zbl 1189.34021

Summary: Consider the following first order lattice system

u ˙ m +(2u m -u m-1 -u m+1 )+λ m u m +f m (u m )=g m ,m,

which is perturbed by the ε-small two order term

εu ¨ m +u ˙ m +(2u m -u m-1 -u m+1 +λ m u m +f m (u m )=g m ,m·

Under certain conditions on f m , λ m and g m , the original systems and the ε-small perturbed systems have global attractors 𝒜 in 2 and 𝒜 ε in 2 × 2 , respectively, and 𝒜 can be naturally embedded into a compact set 𝒜 0 in 2 × 2 . We prove the upper semicontinuity of 𝒜 0 with respect to the attractors 𝒜 ε at zero by showing that for any neighborhood 𝒪(𝒜 0 ) of 𝒜 0 , 𝒜 ε enters 𝒪(𝒜 0 ) if ε is small enough.

MSC:
34A33Lattice differential equations
34E15Asymptotic singular perturbations, general theory (ODE)
34D45Attractors