Large Deviation Principle for Stochastic Thermoelastic System Coupled Sine-Gordon Equation Driven by Lévy Noise

This work discusses the application of large deviation principle for a stochastic nonlinear thermoelastic system coupled Sine-Gordon equation driven by Lévy noise. This is done using weak convergence approach formulated by Dupuis and Ellis wherein Laplace principle and large deviation principle are considered equivalent under specific space settings. Initially, the compactness of solution of the control system corresponding to the original system is proved. The proof is completed by ensuring that the solutions of the controlled stochastic system weakly converges to that of the controlled deterministic system with the aid of the estimate of the solution obtained prior.