Lévy噪声驱动的随机广义多孔介质方程的大偏差
Large Deviations for Stochastic Generalized Porous Media Equations driven by Lévy Noise
AI总结：
本文在无Gelfand三元组嵌入紧性假设下，用新程序证明Lévy噪声驱动、负定自伴算子广义随机多孔介质方程的LDP，并涵盖Stefan问题及多类算子。
摘要：
我们在σ有限测度空间(E, B(E), μ)上，为一类由Lévy型噪声驱动的随机多孔介质方程建立了大偏差原理（LDP），其中Laplacian被一个负定自伴算子替代。本文的主要贡献之一是我们不假设相应Gelfand三元组中嵌入的紧性；为弥补这一推广，我们给出了一种新的程序。这是首篇在无紧性条件下处理带Lévy噪声的随机演化方程LDP的论文。系数Ψ被假设满足非递减Lipschitz非线性，因此该情形涵盖的一个重要物理问题是Stefan问题。许多负定自伴算子的例子都适用于我们的结果，例如，对于开集E⊂ℝᵈ，L=Laplacian或分数阶Laplacian，即L=-(-Δ)^α，α∈(0,1]；广义Schrödinger算子，即L=Δ+2(∇ρ/ρ)·∇；分形上的Laplacian也包含在内。
英文摘要：
We establish a large deviation principle (LDP) for a class of stochastic porous media equations driven by Lévy-type noise on a $σ$-finite measure space $(E,\mathcal{B}(E),μ)$, 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 $Ψ$ 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 $E\subset\Bbb{R}^d$, $L=$ Laplacian or fractional Laplacians, i.e., $L=-(-Δ)^α,\ α\in(0,1]$, generalized Schrödinger operators, i.e., $L=Δ+2\frac{\nabla ρ}ρ\cdot\nabla$, Laplacians on fractals is also included.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
