Open AccessLarge deviations for stochastic Kuramoto–Sivashinsky equation with multiplicative noise
Author(s) -
Gregory Amali Paul Rose,
M. Suvinthra,
K. Balachandran
Publication year - 2021
Publication title -
nonlinear analysis
Language(s) - English
Resource type - Journals
eISSN - 2335-8963
pISSN - 1392-5113
DOI - 10.15388/namc.2021.26.24178
Subject(s) - mathematics , partial differential equation , multiplicative function , stochastic differential equation , multiplicative noise , mathematical analysis , large deviations theory , noise (video) , nonlinear system , convergence (economics) , parabolic partial differential equation , stochastic partial differential equation , instability , first order partial differential equation , statistical physics , physics , computer science , statistics , signal transfer function , digital signal processing , quantum mechanics , artificial intelligence , mechanics , analog signal , economics , image (mathematics) , economic growth , computer hardware
The Kuramoto–Sivashinsky equation is a nonlinear parabolic partial differential equation, which describes the instability and turbulence of waves in chemical reactions and laminar flames. The aim of this work is to prove the large deviation principle for the stochastic Kuramoto–Sivashinsky equation driven by multiplicative noise. To establish the large deviation principle, the weak convergence approach is used, which relies on proving basic qualitative properties of controlled versions of the original stochastic partial differential equation.