We establish the existence and uniqueness of strong solutions to stochastic porous media equations driven by Lévy noise on a \(\sigma \)-finite measure space \((E,{\mathcal {B}}(E),\mu )\), and with the Laplacian replaced by a negative definite self-adjoint operator. The coefficient \(\Psi \) is only assumed to satisfy the increasing Lipschitz nonlinearity assumption, without the restriction \(r\Psi (r)\rightarrow \infty \) as \(r\rightarrow \infty \) for \(L^2(\mu )\)-initial data. We also extend the state space, which avoids the transience assumption on L or the boundedness of \(L^{-1}\) in \(L^{r+1}(E,{\mathcal {B}}(E),\mu )\) for some \(r\ge 1\). Examples of the negative definite self-adjoint operators include fractional powers of the Laplacian, i.e., \(L=-(-\Delta )^\alpha ,\ \alpha \in (0,1]\), generalized \(\mathrm Schr\ddot{o}dinger\) operators, i.e., \(L=\Delta +2\frac{\nabla \rho }{\rho }\cdot \nabla \), and Laplacians on fractals.

我们在\(\sigma \) -有限测度空间\((E,{\mathcal {B}}(E),\mu)\上建立了由Lévy噪声驱动的随机多孔介质方程的强解的存在性和唯一性)，并用负定自伴随算子代替拉普拉斯算子。系数\(\Psi \)仅假设满足递增的 Lipschitz 非线性假设，没有限制\(r\Psi (r)\rightarrow \infty \) as \(r\rightarrow \infty \) for \(L ^2(\mu )\) -初始数据。我们还扩展了状态空间，这避免了L上的瞬态假设或\(L^{-1}\)在\(L^{r+1}(E,{\mathcal {B}}(E),\mu )\)对于某些\(r\ge 1\)。负定自伴随算子的例子包括拉普拉斯算子的分数幂，即\(L=-(-\Delta )^\alpha ,\ \alpha \in (0,1]\)，广义\(\mathrm Schr\ddot{o}dinger\)运算符，即\(L=\Delta +2\frac{\nabla \rho }{\rho }\cdot \nabla \)和分形上的拉普拉斯算子。