Large deviation principle for stochastic Burgers type equation with reflection
The authors consider a stochastic Burgers type equation on the interval \([0,1]\) with Dirichlet boundary condition and reflection. The purpose is to establish a small-noise large deviation principle for the solutions, by using the weak convergence approach. The authors adopt a new sufficient condition for the weak convergence criteria proved by \textit{A. Matoussi} et al. [Appl. Math. Optim. 83, No. 2, 849--879 (2021; Zbl 1470.60188)]. The main difficulty in the proof is to show global well-posedness and continuity of the skeleton equation, due to the highly nonlinear coefficient and the singularity caused by reflection. The authors overcome these difficulties by introducing penalized skeleton equations and showing that the limit of penalized solutions gives rise to a solution of the skeleton equation.
scientific article; zbMATH DE number 7461706
scientific article