Scholarship 15/06131-5 - Problema de Cauchy - BV FAPESP
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Study of solutions to some non-linear evolution equations of dispersive type

Grant number: 15/06131-5
Support Opportunities:Scholarships in Brazil - Doctorate
Start date until: August 01, 2015
End date until: July 31, 2020
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Agreement: Coordination of Improvement of Higher Education Personnel (CAPES)
Principal Investigator:Mahendra Prasad Panthee
Grantee:Francisco Javier Vielma Leal
Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Associated scholarship(s):18/18883-0 - On the controllability and stabilization of the Benjamin equation and its generalization on a periodic domain, BE.EP.DR

Abstract

During the working programme, we are interested in studying the existence and qualitative properties of solutions to non-linear dispersive type equations. In particular, the focus of our study is on issues such as well-posedness of the associated Cauchy problem, stabilization, controllability, existence and stability of solitary wave solutions. Long time behavior, especially for the low-regularity data, will also be considered. Our solution method may consists of Viscosity method, Iteration (Picard) method, Fourier transform restriction norm method, High-low frequency method and recently developed I-method. (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)
PANTHEE, M.; LEAL, F. VIELMA. On the controllability and stabilization of the Benjamin equation on a periodic domain. ANNALES DE L' INSTITUT HENRI POINCARÉ-ANALYSE NON LINÉAIRE, v. 38, n. 5, p. 1605-1652, . (16/25864-6, 15/06131-5)
PANTHEE, MAHENDRA; VIELMA LEAL, FRANCISCO J.. On the controllability and stabilization of the linearized Benjamin equation on a periodic domain. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, v. 51, . (15/06131-5, 18/18883-0)
Academic Publications
(References retrieved automatically from State of São Paulo Research Institutions)
LEAL, Francisco Javier Vielma. Estudo das soluções para algumas equações de evolução não-lineares do tipo dispersivo. 2020. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica Campinas, SP.

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