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Local and global behaviour of solutions of dispersive equations

Grant number: 20/10185-1
Support type:Scholarships in Brazil - Post-Doctorate
Effective date (Start): October 01, 2021
Effective date (End): September 30, 2022
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal researcher:Ademir Pastor Ferreira
Grantee:Luccas Cassimiro Campos
Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Associated research grant:19/02512-5 - Systems and partial differential equations, AP.TEM


We propose the study of the local ang global behavior of solutions to certain equations which are relevant, both from the physical and the mathematical point of view. Modern techniques, as the study of the linearized operator associated to some ground state may be used to determine if certain initial data give rise to finite-time blow-up solutions or to solutions that scatter in space. These techniques are virtually capable of being used to classify all the solutions to the correspondent equations which lie at a mass-energy threshold. Such research topics are of international relevance, and several references are given in the text (including recent advances in the state-of-art). The proposed research problems are either completely open, or have been only partially answered and we believe that ideas based on the aforementioned techniques might be the key to the answers. Given the relevance, the currentness and the familiarity that both the proposed advisor and the candidate have with the topic, together with being part of an international collaborators network, we believe that this project will be very fruitful, bringing positive results to the best understanding of these models. (AU)

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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)
CAMPOS, LUCCAS; CARDOSO, MYKAEL. Blowup and scattering criteria above the threshold for the focusing inhomogeneous nonlinear Schrodinger equation. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, v. 28, n. 6 DEC 2021. Web of Science Citations: 0.

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