Moderate Deviation Principle For Stochastic Partial Differential Equations With A Dynamical Boundary Driven By Lévy Noises

This thesis concerns with two kinds of stochastic partial differential equations with a random dynamical boundary condition driven by Lévy noises.The main purpose is to establish their moderate deviation principle.Firstly,it investigates a stochastic nonlinear wave equation with a random dynamical boundary condition driven by multiplicative Lévy noises.Since the interaction of the Lévy jump noises disturbing and the singular perturbing not only affects the physical medium but also appears on its boundary,it is difficult to prove the tightness of stochastic systems.By seeking a convergence relation to balance the deviation scale and the singular perturbation,it improves the regularity of the system.Employing the stochastic control argument,it further derives the tightness of the system by constructing the equivalent form of the deviation system.With the help of the weak convergence method and a splitting skill,it establishes the moderate deviation principle of this system.Secondly,it also focuses on a stochastic Cahn-Hilliard equation with a random dynamical boundary condition driven by multiplicative Lévy noises.Due to the disturbance of Lévy jump noises both in the domain and on its boundary,the system requires a higher regularity.By constructing product function spaces,the regularity of the deviation systems is improved.Applying the stochastic control argument,it proves the boundedness of stochastic controlled processes and deduces the tightness of deviation processes by the splitting method.Based on the weak convergence approach,it finally establishes the moderate deviation underlying the verification of two moderate deviation conditions,which bridges the gap between the central limit and large deviation.