Local and global behaviour of solutions of dispersive equations

• Grant number: 20/10185-1
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: October 01, 2021
• End date: August 29, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Ademir Pastor Ferreira
• Grantee: Luccas Cassimiro Campos
• Host 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

Abstract

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)

Scientific publications

(4)

(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; GUZMAN, CARLOS M.. Scattering for the non-radial inhomogenous biharmonic NLS equation. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, v. 61, n. 4, p. 15-pg., 2022-08-01. (20/10185-1)

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. (20/10185-1)

CAMPOS, LUCCAS; FARAH, LUIZ GUSTAVO; ROUDENKO, SVETLANA. Threshold solutions for the nonlinear Schrodinger equation. REVISTA MATEMATICA IBEROAMERICANA, v. 38, n. 5, p. 72-pg., 2022-01-01. (20/10185-1)

CAMPOS, LUCCAS; MURPHY, JASON; VAN HOOSE, TIM. Averaging for the 2d dispersion-managed NLS. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, v. N/A, p. 16-pg., 2023-07-19. (20/10185-1)