System of partial differential equations with convolution terms and non-local nonlinearity describing oscillations of plate due to Berger's approach and with accounting for thermal regime in terms of Coleman-Gurtin and Gurtin-Pipkin law and fading memory of material is considered. The equation is transformed into a dynamical system in a suitable Hilbert space, which asymptotic behavior is analysed. Existence of a compact global attractor in this dynamical system and some of its properties are proved in this paper. Main tool in analysis of asymptotic behavior is stabilizability inequality.
|Original language||English (US)|
|Number of pages||32|
|Journal||Communications on Pure and Applied Analysis|
|State||Published - Jan 2010|
All Science Journal Classification (ASJC) codes
- Applied Mathematics