Large Deviations for Stochastic Generalized Porous Media Equations Driven by Lévy Noise
Weina Wu, Jianliang Zhai · SIAM Journal on Mathematical Analysis · 2024
Abstract. We establish a large deviation principle (LDP) for a class of stochastic porous media equations driven by Lévy-type noise on a [Formula: see text]-finite measure space [Formula: see text], with the Laplacian replaced by a negative definite self-adjoint operator. One of the main contributions of this paper is that we do not assume the compactness of embeddings in the corresponding Gelfand triple, and to compensate for this generalization, a new procedure is provided. This is the first paper to deal with LDPs for stochastic evolution equations with Lévy noise without compactness conditions. The coefficient [Formula: see text] is assumed to satisfy nondecreasing Lipschitz nonlinearity, so an important physical problem covered by this case is the Stefan problem. Numerous examples of negative definite self-adjoint operators are applicable to our results, for example, for open [Formula: see text], [Formula: see text] Laplacian or fractional Laplacians (i.e., [Formula: see text], [Formula: see text]), and generalized Schrödinger operators (i.e., [Formula: see text]); Laplacians on fractals is also included.