| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Dept Matemat, BR-13560970 Sao Carlos, SP - Brazil
[2] Silesian Univ, Inst Math, PL-40007 Katowice - Poland
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY; v. 361, n. 5, p. 2567-2586, 2009. |
| Web of Science Citations: | 10 |
| Abstract | |
A class of semilinear evolution equations of the second order in time of the form u(tt)+Au+mu Au(t)+Au(tt) = f(u) is considered, where -A is the Dirichlet Laplacian, 92 is a smooth bounded domain in R(N) and f is an element of C(1) (R, R). A local well posedness result is proved in the Banach spaces W(0)(1,p)(Omega)xW(0)(1,P)(Omega) when f satisfies appropriate critical growth conditions. In the Hilbert setting, if f satisfies all additional dissipativeness condition, the nonlinear Semigroup of global solutions is shown to possess a gradient-like attractor. Existence and regularity of the global attractor are also investigated following the unified semigroup approach, bootstrapping and the interpolation-extrapolation techniques. (AU) | |
| FAPESP's process: | 03/10042-0 - Nonlinear dynamical systems and applications |
| Grantee: | Alexandre Nolasco de Carvalho |
| Support Opportunities: | PRONEX Research - Thematic Grants |