Transportation cost inequalities for stochastic reaction-diffusion equations with L\'evy noises and non-Lipschitz reaction terms

For stochastic reaction-diffusion equations with L'evy noises and non-Lipschitz reaction terms, we prove that $W_{1}H$ transportation cost inequalities hold for their invariant probability measures and for their process-level laws on the path space with respect to the $L^1$-metric. The proofs are based on the Galerkin approximations.