Nonlinear dispersive evolution equations and applications

• Grant number: 13/08050-7
• Support Opportunities: Regular Research Grants
• Start date: July 01, 2013
• End date: June 30, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Ademir Pastor Ferreira
• Grantee: Ademir Pastor Ferreira
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

We are concerned with three main issues in the theory of nonlinear dispersive equations: (a) existence of traveling waves, (b) stability/instability of traveling waves, and (c) local well-posedness and global behavior of solutions. The project is inserted in a new field of research and its main contribution lies on the understanding of the dynamics governed by dispersive evolution equations. We will employ techniques from classical analysis to recent developments in modern harmonic analysis. (AU)

Scientific publications

(6)

(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)

ESFAHANI, AMIN; PASTOR, ADEMIR. Well-posedness and orbital stability of traveling waves for the Schrodinger-improved Boussinesq system. Nonlinear Analysis: Real World Applications, v. 22, p. 206-218, APR 2015. (13/08050-7)

ESFAHANI, AMIN; PASTOR, ADEMIR. Well-posedness and orbital stability of traveling waves for the Schrodinger-improved Boussinesq system. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, v. 22, p. 13-pg., 2015-04-01. (13/08050-7)

DE ANDRADE, THIAGO PINGUELLO; PASTOR, ADEMIR. Orbital stability of periodic traveling-wave solutions for the regularized Schamel equation. PHYSICA D-NONLINEAR PHENOMENA, v. 317, p. 43-58, MAR 1 2016. (13/08050-7)

CUNHA, ALYSSON; PASTOR, ADEMIR. The IVP for the Benjamin-Ono-Zakharov-Kuznetsov equation in low regularity Sobolev spaces. Journal of Differential Equations, v. 261, n. 3, p. 2041-2067, AUG 5 2016. (13/08050-7)

CUNHA, ALYSSON; PASTOR, ADEMIR. The IVP for the Benjamin-Ono-Zakharov-Kuznetsov equation in weighted Sobolev spaces. Journal of Mathematical Analysis and Applications, v. 417, n. 2, p. 660-693, SEP 15 2014. (13/08050-7)

NATALI, FABIO; PASTOR, ADEMIR; CRISTOFANI, FABRICIO. Orbital stability of periodic traveling-wave solutions for the log-KdV equation. Journal of Differential Equations, v. 263, n. 5, p. 2630-2660, SEP 5 2017. (13/08050-7)