| Full text | |
| Author(s): |
Carvalho, Alexandre N.
;
Lappicy, Phillipo
;
Moreira, Estefani M.
;
Oliveira-Sousa, Alexandre N.
Total Authors: 4
|
| Document type: | Journal article |
| Source: | Journal of Differential Equations; v. 416, p. 34-pg., 2024-10-31. |
| Abstract | |
Inertial manifold theory, saddle point property and exponential dichotomy have been treated as different topics in the literature with different proofs. As a common feature, they all have the purpose of 'splitting' the space to understand the dynamics. We present a unified proof for the inertial manifold theorem, which as a local consequence yields the saddle-point property with a fine structure of invariant manifolds and the roughness of exponential dichotomy. In particular, we use these tools in order to establish the hyperbolicity of certain global solutions for non-autonomous parabolic partial differential equations. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies. (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: | 17/07882-0 - Einstein constraints and differential equations on the sphere |
| Grantee: | Phillipo Lappicy Lemos Gomes |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 20/14075-6 - Dynamical systems and their attractors under perturbations |
| Grantee: | Alexandre Nolasco de Carvalho |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 20/00104-4 - Comparison results between solutions of autonomous and non-autonomous problems: an investigation about existence of non-autonomos equilibria |
| Grantee: | Estefani Moraes Moreira |
| Support Opportunities: | Scholarships abroad - Research Internship - Doctorate |
| FAPESP's process: | 18/00065-9 - Gradient structure of skew product semiflows |
| Grantee: | Estefani Moraes Moreira |
| Support Opportunities: | Scholarships in Brazil - 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: | 18/18703-1 - Attractors for fully nonlinear parabolic equations and non-autonomous equations |
| Grantee: | Phillipo Lappicy Lemos Gomes |
| Support Opportunities: | Scholarships abroad - Research Internship - Post-doctor |