Open AccessA Fokker-Planck type approximation of parabolic PDEs with oblique boundary data
Author(s) -
Damon Alexander,
In-Won Kim
Publication year - 2015
Publication title -
transactions of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.798
H-Index - 100
eISSN - 1088-6850
pISSN - 0002-9947
DOI - 10.1090/tran/6521
Subject(s) - mathematics , bounded function , domain (mathematical analysis) , mathematical analysis , oblique case , fokker–planck equation , parabolic partial differential equation , convergence (economics) , boundary (topology) , type (biology) , space (punctuation) , zero (linguistics) , partial differential equation , ecology , philosophy , linguistics , biology , economics , economic growth
We consider solutions of quasi-linear parabolic PDEs with zero oblique boundary data in a bounded domain. Our main result states that the solutions can be approximated by solutions of a Fokker-Planck type PDE in the whole space with a penalizing drift term which also converges to zero outside the original domain. The convergence is locally uniform, and optimal error estimates are obtained.