| Grant number: | 16/04925-7 |
| Support type: | Regular Research Grants |
| Duration: | July 01, 2016 - June 30, 2018 |
| Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Analysis |
| Principal Investigator: | Juliana Fernandes da Silva Pimentel |
| Grantee: | Juliana Fernandes da Silva Pimentel |
| Home Institution: | Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil |
Abstract
Despite being a stimulating and ongoing topic of research, the theory of attractors for infinite-dimensional dynamical systems has been relied, for a long time, on a crucial existence assumption of a compact absorbing set for the trajectories. Meanwhile, dynamical systems not having bounded attractors due to the existence of unbounded, and therefore not absorbed, trajectories are also of great interest. Motivated by that, in this research project we propose to investigate and develop a general theory of unbounded attractors, both in autonomous and nonautonomous settings. This direction of research is motivated, in particular, by the study of the attractors in evolution equations when the nonlinearity is not dissipative. With that in mind, we plan to consider a scalar nonautonomous parabolic equation, with no dissipativity properties, as our toy model. Since, trajectories might become unbounded in finite or infinite time, it is inevitable not addressing blow-up phenomena for evolution equations. In this line, we aim at exploring the possible asymptotic regimes and profiles appearing on semilinear nondissipative heat equations, defined on $n$-dimensional domains. (AU)