Generalized Functions and Irregular Solutions of Linear and Nonlinear Equations and Applications

• Grant number: 12/15780-9
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: December 01, 2012
• End date: November 30, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Orlando Stanley Juriaans
• Grantee: Mathilde Francoise Charlotte Colombeau-Fonteyne
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

We sill define new algebras of generalized functions and use them to study irregular solutions of PDEs and make numerical simulations to sustain the results obtained.Applications in engineering problems will be considered and the results obtained will be compared with existing or recently obtained results.

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)

ABREU, EDUARDO; COLOMBEAU, MATHILDE; PANOV, EVGENY YU. Approximation of entropy solutions to degenerate nonlinear parabolic equations. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, v. 68, n. 6, DEC 2017. (12/15780-9)

COLOMBEAU, M.. Asymptotic study of the initial value problem to a standard one pressure model of multifluid flows in nondivergence form. Journal of Differential Equations, v. 260, n. 1, p. 197-217, JAN 5 2016. (12/15780-9)

ABREU, EDUARDO; COLOMBEAU, MATHILDE; PANOV, EUGENY. Weak asymptotic methods for scalar equations and systems. Journal of Mathematical Analysis and Applications, v. 444, n. 2, p. 1203-1232, DEC 15 2016. (12/15780-9)

COLOMBEAU, M.. Approximate solutions to the initial value problem for some compressible flows. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, v. 66, n. 5, p. 2575-2599, OCT 2015. (12/15780-9)

COLOMBEAU, M.. Weak asymptotic methods for 3-D self-gravitating pressureless fluids. Application to the creation and evolution of solar systems from the fully nonlinear Euler-Poisson equations. Journal of Mathematical Physics, v. 56, n. 6, JUN 2015. (12/15780-9)

COLOMBEAU, M.. Irregular shock waves formation as continuation of analytic solutions. APPLICABLE ANALYSIS, v. 94, n. 9, p. 1800-1820, SEP 2 2015. (12/15780-9)