Topics in stochastic partial diferential equations

• Grant number: 15/04723-2
• Support Opportunities: Regular Research Grants
• Start date: September 01, 2015
• End date: August 31, 2017
• 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 research grant(s): 15/50456-6 - Regularity in law of first order stochastic partial differential equations, AP.R SPRINT

Abstract

We are interested in to study generalized solutions of stochastic partial diferential Equation. In particular, we are interested in generalized solutions of the KPZ equationvia the theory of distributions and algebras of generalized functions. Also, we are interested in to study the stochastic transport equation and stochastic hyperbolic equations of first order. The order part of this project is to study the numerical methods and computation simulation of these equations. (AU)

Scientific publications

(10)

(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)

SIMON, MARIELLE; OLIVERA, CHRISTIAN. Non-local Conservation Law from Stochastic Particle Systems. Journal of Dynamics and Differential Equations, v. 30, n. 4, p. 1661-1682, DEC 2018. (15/07278-0, 15/04723-2)

FLANDOLI, FRANCO; OLIVERA, CHRISTIAN. Well-posedness of the vector advection equations by stochastic perturbation. JOURNAL OF EVOLUTION EQUATIONS, v. 18, n. 2, p. 277-301, JUN 2018. (15/04723-2)

MOLLINEDO, DAVID A. C.; OLIVERA, CHRISTIAN. Stochastic continuity equation with nonsmooth velocity. Annali di Matematica Pura ed Applicata, v. 196, n. 5, p. 1669-1684, OCT 2017. (15/07278-0, 15/04723-2)

NEVES, WLADIMIR; OLIVERA, CHRISTIAN. Stochastic continuity equations-A general uniqueness result. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 47, n. 2, p. 631-639, JUN 2016. (15/04723-2)

FLANDOLI, FRANCO; LEIMBACH, MATTI; OLIVERA, CHRISTIAN. Uniform convergence of proliferating particles to the FKPP equation. Journal of Mathematical Analysis and Applications, v. 473, n. 1, p. 27-52, MAY 1 2019. (15/04723-2)

CLARKE, JORGE; OLIVERA, CHRISTIAN; TUDOR, CIPRIAN. THE TRANSPORT EQUATION AND ZERO QUADRATIC VARIATION PROCESSES. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, v. 21, n. 9, p. 12-pg., 2016-11-01. (15/04723-2)

CLARKE, JORGE; OLIVERA, CHRISTIAN; TUDOR, CIPRIAN. THE TRANSPORT EQUATION AND ZERO QUADRATIC VARIATION PROCESSES. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, v. 21, n. 9, SI, p. 2991-3002, NOV 2016. (15/04723-2)

MOLLINEDO, DAVID A. C.; OLIVERA, CHRISTIAN. Well-Posedness of the Stochastic Transport Equation with Unbounded Drift. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 48, n. 4, p. 663-677, DEC 2017. (15/07278-0, 15/04723-2)

CATUOGNO, P.; COLOMBEAU, J. F.; OLIVERA, C.. Generalized solutions of the multidimensional stochastic Burgers equation. Journal of Mathematical Analysis and Applications, v. 464, n. 2, p. 1375-1382, AUG 15 2018. (15/07278-0, 12/18940-7, 15/04723-2)

CATUOGNO, PEDRO; MOLINA, SANDRA; OLIVERA, C.. Generalized functions and Laguerre expansions. MONATSHEFTE FUR MATHEMATIK, v. 184, n. 1, p. 51-75, SEP 2017. (15/07278-0, 15/04723-2)