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Stochastic Partial Differential Equations and Particle Systems

Grant number: 17/17670-0
Support Opportunities:Regular Research Grants
Duration: November 01, 2017 - October 31, 2019
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal Investigator:Christian Horacio Olivera
Grantee:Christian Horacio Olivera
Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Associated researchers: Ciprian Tudor ; David Alexander Chipana Mollinedo ; Jean-François Claude Colombeau ; Jorge Clarke ; Marielle Simon ; Pedro Jose Catuogno
Associated grant(s):18/15258-7 - Approximation of partial differential equations by stochastic particle systems with weak and moderate interaction, AP.R SPRINT

Abstract

This research project presents in a global way the research interests of the proponent team. In fact, we are interested in studying existence, uniqueness and regularity in the law of stochastic partial differential equations.Another important part of the project is to study the propagation of chaos of particle systems with moderate interaction. (AU)

Articles published in Agência FAPESP Newsletter about the research grant:
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VEICULO: TITULO (DATA)

Scientific publications (14)
(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)
MOLLINEDO, DAVID A. C.; OLIVERA, CHRISTIAN; TUDOR, CIPRIAN A.. Existence and Smoothness of the Density for the Stochastic Continuity Equation. Results in Mathematics, v. 74, n. 1, . (15/07278-0, 17/17670-0)
OLIVERA, CHRISTIAN. Well-posedness of the non-local conservation law by stochastic perturbation. MANUSCRIPTA MATHEMATICA, v. 162, n. 3-4, p. 367-387, . (15/07278-0, 17/17670-0)
OLIVERA, CHRISTIAN. Regularization by Noise in One-Dimensional Continuity Equation. POTENTIAL ANALYSIS, v. 51, n. 1, p. 23-35, . (17/17670-0)
NEVES, WLADIMIR; OLIVERA, CHRISTIAN. Initial-boundary value problem for stochastic transport equations. STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS, v. 9, n. 3, p. 674-701, . (15/07278-0, 17/17670-0, 13/15795-9)
OLIVERA, CHRISTIAN; SHAMAROVA, EVELINA. Gaussian density estimates for solutions of fully coupled forward-backward SDEs. Mathematische Nachrichten, v. 293, n. 8, p. 11-pg., . (17/17670-0, 15/07278-0)
NEVES, WLADIMIR; OLIVERA, CHRISTIAN. Initial-boundary value problem for stochastic transport equations. STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS, . (13/15795-9, 15/07278-0, 17/17670-0)
DE LA CRUZ, H.; OLIVERA, C.. An explicit numerical scheme for the computer simulation of the stochastic transport equation. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 110, p. 14-pg., . (17/17670-0, 15/07278-0)
OLIVERA, CHRISTIAN; TUDOR, CIPRIAN A.. Existence and Besov regularity of the density for a class of SDEs with Volterra noise. COMPTES RENDUS MATHEMATIQUE, v. 357, n. 7, p. 636-645, . (15/07278-0, 17/17670-0)
CLARKE, JORGE; OLIVERA, CHRISTIAN. LOCAL L-p-SOLUTION FOR SEMILINEAR HEAT EQUATION WITH FRACTIONAL NOISE. ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, v. 45, p. 305-312, . (15/07278-0, 17/17670-0)
FERRARIO, BENEDETTA; OLIVERA, CHRISTIAN. 2D Navier-Stokes equation with cylindrical fractional Brownian noise. Annali di Matematica Pura ed Applicata, v. 198, n. 3, p. 1041-1067, . (15/07278-0, 17/17670-0)
OLIVERA, CHRISTIAN; TUDOR, CIPRIAN. Density for solutions to stochastic differential equations with unbounded drift. BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS, v. 33, n. 3, p. 520-531, . (15/07278-0, 17/17670-0)
FERRARIO, BENEDETTA; OLIVERA, CHRISTIAN. L-p-solutions of the Navier-Stokes equation with fractional Brownian noise. AIMS MATHEMATICS, v. 3, n. 4, p. 539-553, . (15/07278-0, 17/17670-0)
OLIVERA, CHRISTIAN. Probabilistic representation for mild solution of the Navier-Stokes equations. MATHEMATICAL RESEARCH LETTERS, v. 28, n. 2, p. 563-573, . (15/07278-0, 17/17670-0)
OLIVERA, CHRISTIAN; SHAMAROVA, EVELINA. Gaussian density estimates for solutions of fully coupled forward-backward SDEs. Mathematische Nachrichten, v. 293, n. 8, p. 1554-1564, . (17/17670-0, 15/07278-0)

Please report errors in scientific publications list by writing to: gei-bv@fapesp.br.