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Dynamics of systems on infinite lattices
- Source :
-
Journal of Differential Equations . Feb2006, Vol. 221 Issue 1, p224-245. 22p. - Publication Year :
- 2006
-
Abstract
- Abstract: The dynamics of infinite-dimensional lattice systems is studied. A necessary and sufficient condition for asymptotic compactness of lattice dynamical systems is introduced. It is shown that a lattice system has a global attractor if and only if it has a bounded absorbing set and is asymptotically null. As an application, it is proved that the lattice reaction–diffusion equation has a global attractor in a weighted space, which is compact as well as contains traveling waves. The upper semicontinuity of global attractors is also obtained when the lattice reaction–diffusion equation is approached by finite-dimensional systems. [Copyright &y& Elsevier]
- Subjects :
- *DIFFUSION
*PROPERTIES of matter
*SEMICONDUCTOR doping
*SOLID solutions
Subjects
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 221
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 19392086
- Full Text :
- https://doi.org/10.1016/j.jde.2005.01.003