| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Fed Paraiba, Dept Matemat, BR-58051900 Joao Pessoa, Paraiba - Brazil
[2] Univ Sao Paulo, Dept Matemat, Inst Ciencias Matemat & Comp, Campus Sao Carlos, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil
[3] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Carlos, SP - Brazil
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B; v. 25, n. 11, p. 4221-4255, SEP 2020. |
| Web of Science Citations: | 0 |
| Abstract | |
In this paper we study the abstract semilinear parabolic problem of the form du/dt + Au = f(u), as the limit of the corresponding fractional approximations du/dt + A(alpha)u = f(u), in a Banach space X, where the operator A : D(A) subset of X -> X is a sectorial operator in the sense of Henry {[}22]. Under suitable assumptions on nonlinearities f : X-alpha -> X (X-alpha := D(A(alpha))), we prove the continuity with rate (with respect to the parameter alpha) for the global attractors (as seen in Babin and Vishik {[}4] Chapter 8, Theorem 2.1). As an application of our analysis we consider a fractional approximation of the strongly damped wave equations and we study the convergence with rate of solutions of such approximations. (AU) | |
| FAPESP's process: | 03/10042-0 - Nonlinear dynamical systems and applications |
| Grantee: | Alexandre Nolasco de Carvalho |
| Support Opportunities: | PRONEX Research - Thematic Grants |
| FAPESP's process: | 14/03686-3 - The dynamics of evolution equations governed by fractional powers of closed operators |
| Grantee: | Flank David Morais Bezerra |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 17/06582-2 - Asymptotic behavior for non-autonomous semilinear problems |
| Grantee: | Marcelo José Dias Nascimento |
| Support Opportunities: | Regular Research Grants |