Generalized functions and stochastic equations

• Grant number: 12/18739-0
• Support Opportunities: Regular Research Grants
• Start date: May 01, 2013
• End date: February 28, 2015
• 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: Jean François Colombeau ; Pedro Jose Catuogno

Abstract

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)

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. (13/15795-9, 12/18739-0)

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. (13/15795-9, 12/18739-0, 12/18780-0)

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. (12/18739-0)

CATUOGNO, P.; OLIVERA, C.. Strong solution of the stochastic Burgers equation. APPLICABLE ANALYSIS, v. 93, n. 3, p. 646-652, MAR 4 2014. (12/18739-0)

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. (12/18739-0)

OLIVERA, CHRISTIAN. Well-posedness of first order semilinear PDEs by stochastic perturbation. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 96, p. 211-215, FEB 2014. (12/18739-0)