| Grant number: | 19/23688-4 |
| Support Opportunities: | Regular Research Grants |
| Start date: | February 01, 2020 |
| End date: | June 30, 2021 |
| Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Analysis |
| Principal Investigator: | Priscila Leal da Silva |
| Grantee: | Priscila Leal da Silva |
| Host Institution: | Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil |
Abstract
The main aim of this project is to investigate properties of solutions of evolutionary differential equations in $1+1$ dimensions (one time and one spatial variables). On the one hand, it is intended to investigate linear stability of solutions of \textit{integrable} equations by making use of a recent method due Degasperis, Lombardo and Sommacal (\textit{Journal of Nonlinear Science}, \textbf{v. 28}, 1251--1291, 2018), where the analysis of instability relies on the investigation of algebraic structures related to the \textit{stability spectra}, obtained from a spectral problem without any participation of boundary conditions. Conversely, another direction aims at understanding local and global existence and uniqueness of solutions in Sobolev and Gevrey spaces, considering \textit{integrable} and \textit{non-integrable} equations that may conserve energy or whose energy can be bounded from below. In general, \textit{non-integrable} equations have considerably less structure and the study of their solutions is a highly non-trivial subject. (AU)
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