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: August 01, 2015
• End date: 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)

Scientific publications

(The scientific publications listed on this page originate from the Web of Science or SciELO databases. Their authors have cited FAPESP grant or fellowship project numbers awarded to Principal Investigators or Fellowship Recipients, whether or not they are among the authors. This information is collected automatically and retrieved directly from those bibliometric databases.)

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, FEB 2020. (15/06131-5, 18/18883-0)

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, SEP-OCT 2021. (16/25864-6, 15/06131-5)

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.