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

Grant number: 12/15780-9
Support Opportunities:Scholarships in Brazil - Post-Doctoral
Effective date (Start): December 01, 2012
Effective date (End): 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.

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

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