Well-posedness and large deviations for a class of SPDEs with Levy noise

作者：Chen, Yong^*; Gao, Hongjun

来源：Journal of Differential Equations, 2017, 263(9): 5216-5252.

DOI：10.1016/j.jde.2017.06.016

• Well-posedness
• Large deviations
• Iterative approximation
• Regularization
• Shallow water equations

In this paper, a class of stochastic partial differential equations (SPDEs) with Levy noise is concerned. Firstly, the local well-posedness is established by the iterative approximation. Then the large deviation principle (LDP) for the regularized SPDEs is obtained by the weak convergence approach. To get the LDP for SPDEs here, an exponential equivalence of the probability measures is proved. The results can be applied to some types of SPDEs such as stochastic Burgers equation, stochastic b-family equation, stochastic modified Novikov equation and stochastic mu-HunterSaxton equation.

• 出版日期2017-11-5
• 单位浙江理工大学; 南京师范大学; 吉林大学