| Full text | |
| Author(s): |
Caraballo, Tomas
;
Carvalho, Alexandre N.
;
Langa, Jose A.
;
Oliveira-Sousa, Alexandre N.
Total Authors: 4
|
| Document type: | Journal article |
| Source: | ASYMPTOTIC ANALYSIS; v. 129, n. 1, p. 27-pg., 2022-01-01. |
| Abstract | |
In this paper, we study stability properties of nonuniform hyperbolicity for evolution processes associated with differential equations in Banach spaces. We prove a robustness result of nonuniform hyperbolicity for linear evolution processes, that is, we show that the property of admitting a nonuniform exponential dichotomy is stable under perturbation. Moreover, we provide conditions to obtain uniqueness and continuous dependence of projections associated with nonuniform exponential dichotomies. We also present an example of evolution process in a Banach space that admits nonuniform exponential dichotomy and study the permanence of the nonuniform hyperbolicity under perturbation. Finally, we prove persistence of nonuniform hyperbolic solutions for nonlinear evolution processes under perturbations. (AU) | |
| FAPESP's process: | 18/10633-4 - A study of structural stability for random attractors |
| Grantee: | Alexandre do Nascimento Oliveira Sousa |
| Support Opportunities: | Scholarships abroad - Research Internship - Doctorate |
| FAPESP's process: | 17/21729-0 - A study about structural stability of atrators for random dynamical systems |
| Grantee: | Alexandre do Nascimento Oliveira Sousa |
| Support Opportunities: | Scholarships in Brazil - Doctorate |
| FAPESP's process: | 18/10997-6 - Robustness of attractors under autonomous or non-autonomous perturbatinos: Structural Stability |
| Grantee: | Alexandre Nolasco de Carvalho |
| Support Opportunities: | Scholarships abroad - Research |