论文标题
由Lévy噪声驱动的随机广义多孔介质方程，Lipschitz非线性增加
Stochastic generalized porous media equations driven by Lévy noise with increasing Lipschitz nonlinearities
论文作者
论文摘要
我们建立了强大解决方案的存在和独特性，以在$σ$ - 罚款噪声上驱动的随机多孔介质方程式，并在$σ$ -finite量度上空间$（E，\ Mathcal {B}（e），μ）$，并由拉普拉基人替换为负面的负面自我接触式操作员。系数$ψ$仅被假定满足不断增加的Lipschitz非线性假设，而无需限制$rψ（r）\ rightarrow \ infty \ as $ r \ rightarrow \ rightarrow \ rightarrow \ for $ l^2（μ）$ - 初始数据。我们还扩展了状态空间，该空间避免了$ l $上的瞬态假设或$ l^{ - 1} $在$ l^{r+1}中的界限（e，\ mathcal {b}（e），μ），μ）$。负面明确的自我接合运算符的示例包括拉普拉斯的分数功能，即$ l = - （ - δ）^α，\α\ in（0,1] $，概括的schrödinger经营者，即$ $ l =δ+δ+δ+2 \ frac {\ nablaρ}ρ\ cd $ cdot \ cd $ cdot \ cd $ cdot \ cdot \ cdot \ cdot \ cdot \ cdot \ cdot \ cd $ \ cdot \ cdot \ cdot \ cdot \ cdot \ cdot \ cdot \ cdot \ cdot \ cd。
We establish the existence and uniqueness of strong solutions to stochastic porous media equations driven by Lévy noise on a $σ$-finite measure space $(E,\mathcal{B}(E),μ)$, and with the Laplacian replaced by a negative definite self-adjoint operator. The coefficient $Ψ$ is only assumed to satisfy the increasing Lipschitz nonlinearity assumption, without the restriction $rΨ(r)\rightarrow\infty$ as $r\rightarrow\infty$ for $L^2(μ)$-initial data. We also extend the state space, which avoids the transience assumption on $L$ or the boundedness of $L^{-1}$ in $L^{r+1}(E,\mathcal{B}(E),μ)$ for some $r\geq1$. Examples of the negative definite self-adjoint operators include fractional powers of the Laplacian, i.e. $L=-(-Δ)^α,\ α\in(0,1]$, generalized Schrödinger operators, i.e. $L=Δ+2\frac{\nabla ρ}ρ\cdot\nabla$, and Laplacians on fractals.
