| Full text | |
| Author(s): |
Lopez-Lazaro, Heraclio
;
Nascimento, Marcelo J. D.
;
Takaessu Jr, Carlos R.
;
Azevedo, Vinicius T.
Total Authors: 4
|
| Document type: | Journal article |
| Source: | Journal of Differential Equations; v. 393, p. 44-pg., 2024-02-20. |
| Abstract | |
This paper aims to study a semilinear transfer equation with a delay term defined over a non-cylindrical domain. We prove the existence and regularity of weak solutions as well as the existence, regularity and finiteness of the fractal dimension of pullback attractors on tempered universes that depend on a nonincreasing function. We address the problem of estimating the fractal dimension of pullback attractors, under current techniques, which consists of readjusting the proof presented in [9, Lemma 1.3] and extending it to families of normed spaces parameterized in time, see Theorem 4.11. (c) 2024 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 22/13001-4 - Finite fractal dimension for non-linear parabolic equations with subdifferential principal part |
| Grantee: | Heraclio Ledgar López Lázaro |
| Support Opportunities: | Scholarships abroad - Research Internship - Post-doctor |
| FAPESP's process: | 22/16305-4 - Long-time dynamics of semilinear problems |
| Grantee: | Marcelo José Dias Nascimento |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 20/14353-6 - Hyperbolicity for quasilinear parabolic problems |
| Grantee: | Carlos Roberto Takaessu Junior |
| Support Opportunities: | Scholarships in Brazil - Doctorate |
| FAPESP's process: | 21/01931-4 - Pullback attractor for non-linear parabolic equations with subdifferential principal part |
| Grantee: | Heraclio Ledgar López Lázaro |
| 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: | 22/02172-2 - Shadowing and hyperbolicity for quasilinear parabolic problems |
| Grantee: | Carlos Roberto Takaessu Junior |
| Support Opportunities: | Scholarships abroad - Research Internship - Doctorate |