论文标题
由Lévy噪声驱动的随机广义多孔培养基方程的大偏差
Large Deviations for Stochastic Generalized Porous Media Equations driven by Lévy Noise
论文作者
论文摘要
我们为一类由Lévy-type噪声驱动的随机多孔媒体方程式建立了一个大偏差原理（LDP），在$σ$ - finite Mesuite space $（e，\ mathcal {b}（e），μ），μ）$中，由Laplacian代替了负面的自我选择者。本文的主要贡献之一是，我们不假定相应的Gelfand三重嵌入的紧凑性，并且为了补偿这种概括，提供了一个新的程序。这是第一篇与LDP处理随机演化方程的论文，并没有紧凑的条件。假定系数$ψ$可以满足非lipschitz非线性的不折衷，因此这种情况涵盖的重要物理问题是Stefan问题。许多负面明确的自动化操作员的示例适用于我们的结果，例如，对于开放$ e \ subset \ bbb {r}^d $，$ l = $ laplacian或分数laplacians，即，即，$ l = - （ - δ） $ l =δ+2 \ frac {\ nablaρ}ρ\ cdot \ nabla $，分形上的laplacians也包括在内。
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.
