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Generalized functions and stochastic equations

Grant number: 12/18739-0
Support type:Regular Research Grants
Duration: May 01, 2013 - February 28, 2015
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal researcher:Christian Horacio Olivera
Grantee:Christian Horacio Olivera
Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Assoc. researchers: Jean François Colombeau ; Pedro Jose Catuogno


Study generalized solutions of stochastic nonlinear equations with rough initial condition via the distribution theory and the algebras of generalized functions. Inspired in the ideas of [9], [10] and [12] we would like to to createlinks between solutions in generalized function algebras and the solutions via the Galerkin method of numerical approximation. In particular, we are interested in generalized solutions of the KPZ equation. (AU)

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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)
FEDRIZZI, ENNIO; NEVES, WLADIMIR; OLIVERA, CHRISTIAN. On a class of stochastic transport equations for L-loc(2) vector fields. ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, v. 18, n. 2, p. 397-419, 2018. Web of Science Citations: 1.
OLIVERA, CHRISTIAN; TUDOR, CIPRIAN A. The density of the solution to the stochastic transport equation with fractional noise. Journal of Mathematical Analysis and Applications, v. 431, n. 1, p. 57-72, NOV 1 2015. Web of Science Citations: 4.
NEVES, WLADIMIR; OLIVERA, CHRISTIAN. Wellposedness for stochastic continuity equations with Ladyzhenskaya-Prodi-Serrin condition. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, v. 22, n. 5, p. 1247-1258, OCT 2015. Web of Science Citations: 8.
CATUOGNO, PEDRO; OLIVERA, CHRISTIAN. Renormalized-generalized solutions for the KPZ equation. INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, v. 17, n. 4 DEC 2014. Web of Science Citations: 0.
CATUOGNO, P.; OLIVERA, C. Strong solution of the stochastic Burgers equation. APPLICABLE ANALYSIS, v. 93, n. 3, p. 646-652, MAR 4 2014. Web of Science Citations: 3.
OLIVERA, CHRISTIAN. Well-posedness of first order semilinear PDEs by stochastic perturbation. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 96, p. 211-215, FEB 2014. Web of Science Citations: 2.

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