Ibragimov's theorem and conservation laws for equations without Lagrangians.

• Grant number: 11/23538-0
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: June 01, 2012
• End date: May 31, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Igor Leite Freire
• Grantee: Júlio Cesar Santos Sampaio
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

In this project we intend to apply the recent concepts on weak self-adjoint and nonlinearly self-adjoint equations formulated by Maria Luz Gandarias and Nail Ibragimov to partial differential equations without Lagrangians. We also intend to determine the subclasses of the nonlinearly self-adjoint equations of important equations in Analysis, Physics and Biomathematics. For the nonlinearly self-adjoint equations we shall establish conservation laws by using their Lie point symmetries and the Ibragimov's theorem on conservation laws.

Scientific publications

(5)

(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)

FREIRE, IGOR LEITE; SANTOS SAMPAIO, JULIO CESAR. On the nonlinear self-adjointness and local conservation laws for a class of evolution equations unifying many models. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 19, n. 2, SI, p. 350-360, FEB 2014. (11/19089-6, 11/23538-0)

SANTOS SAMPAIO, JULIO CESAR; FREIRE, IGOR LEITE. Nonlinear Self-Adjoint Classification of a Burgers-KdV Family of Equations. Abstract and Applied Analysis, 2014. (11/19089-6, 11/23538-0)

DA SILVA, PRISCILA LEAL; FREIRE, IGOR LEITE; SANTOS SAMPAIO, JULIO CESAR. A family of wave equations with some remarkable properties. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SC, v. 474, n. 2210, FEB 2018. (11/23538-0, 14/05024-8, 12/22725-4)

FREIRE, IGOR LEITE; SANTOS SAMPAIO, JULIO CESAR. On the nonlinear self-adjointness and local conservation laws for a class of evolution equations unifying many models. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 19, n. 2, p. 11-pg., 2014-02-01. (11/23538-0, 11/19089-6)

SANTOS SAMPAIO, JULIO CESAR; FREIRE, IGOR LEITE. Nonlinear Self-Adjoint Classification of a Burgers-KdV Family of Equations. Abstract and Applied Analysis, v. N/A, p. 7-pg., 2014-01-01. (11/23538-0, 11/19089-6)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

SAMPAIO, Júlio Cesar Santos. On symmetries and Ibragimov's theory on conservation laws. 2015. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica Campinas, SP.