Properties for solutions of evolution equations

• Grant number: 19/23688-4
• Support Opportunities: Regular Research Grants
• Duration: February 01, 2020 - 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)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

DA SILVA, PRISCILA LEAL; FREIRE, IGOR LEITE. A geometrical demonstration for continuation of solutions of the generalised BBM equation. MONATSHEFTE FUR MATHEMATIK, v. 194, n. 3, AUG 2020. (19/23688-4)

DA SILVA, PRISCILA L.. Local well-posedness and global analyticity for solutions of a generalized 0-equation. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, v. N/A, p. 21-pg., 2022-09-27. (19/23688-4)

DA SILVA, PRISCILA LEAL; FREIRE, IGOR LEITE. Existence, persistence, and continuation of solutions for a generalized 0-Holm-Staley equation. Journal of Differential Equations, v. 320, p. 28-pg., 2022-05-25. (19/23688-4)