zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Exponential attractor and its fractal dimension for a second order lattice dynamical system. (English) Zbl 1192.37107
The authors investigate an exponential attractor with fractal dimension and approximation for a second order lattice dynamical system of nonlinear damping arising from spatial discretization of wave equations in real finite-dimensional spaces using basic theories of differential equations and semigroups.
37L60Lattice dynamics (infinite-dimensional dissipative systems)
37C70Attractors and repellers, topological structure
37L30Attractors and their dimensions, Lyapunov exponents
[1]Afraimovich, V. S.; Chow, S. N.; Hale, J. K.: Synchronization in lattices of coupled oscillations, Phys. D 103, 442-451 (1997) · Zbl 1194.34056 · doi:10.1016/S0167-2789(96)00276-X
[2]Babin, A. V.; Nicolaenko, B.: Exponential attractors for reaction diffusion equations in unbounded domains, J. dynam. Differential equations 7, 567-590 (1995) · Zbl 0846.35061 · doi:10.1007/BF02218725
[3]Bates, P. W.; Lu, K.; Wang, B.: Attractors for lattice dynamical systems, Internat. J. Bifur. chaos 11, 143-153 (2001) · Zbl 1091.37515 · doi:10.1142/S0218127401002031
[4]Chate, H.; Courbage, M.: Lattice systems, Phys. D 103, 1-612 (1997)
[5]Fan, X.; Wang, Y.: Attractors for a second order nonautonomous lattice dynamical system with nonlinear dampping, Phys. lett. A 365, 17-27 (2007) · Zbl 1203.37122 · doi:10.1016/j.physleta.2006.12.045
[6]A. Eden, C. Foias, B. Nicolaenko, R. Temam, Inertial sets for dissipative evolution equations, IMA preprint series, 1991
[7]Eden, A.; Foias, C.; Kalantarov, V.: A remark on two constructions of exponential attractors for α-contractions, J. dynam. Differential equations 1, 37-45 (1998) · Zbl 0898.58035 · doi:10.1023/A:1022636328133
[8]Wang, B.: Asymptotic behavior of non-autonomous lattice systems, J. math. Anal. appl. 331, 121-136 (2007) · Zbl 1112.37076 · doi:10.1016/j.jmaa.2006.08.070
[9]Zhao, C.; Zhou, S.: Compact kernel sections for nonautonomous Klein – Gordon – Schrödinger equations on infinite lattices, J. math. Anal. appl. 332, 32-56 (2007) · Zbl 1113.37057 · doi:10.1016/j.jmaa.2006.10.002
[10]Zhou, S.: Attractors for second order lattice dynamical systems, J. differential equations 179, 605-624 (2002) · Zbl 1002.37040 · doi:10.1006/jdeq.2001.4032
[11]Zhou, S.: Attractors for second-order lattice dynamical systems with damping, J. math. Phys. 43, No. 1, 452-465 (2002) · Zbl 1059.37063 · doi:10.1063/1.1418719
[12]Zhou, S.: Attractors for lattice systems corresponding to evolution equations, Nonlinearity 15, 1-17 (2002) · Zbl 1002.37039 · doi:10.1088/0951-7715/15/4/307