We consider a class of generalized stochastic porous media equations with multiplicative Lipschitz continuous noise. These equations can be related to physical models exhibiting self-organized criticality. We show that these SPDEs have unique SVI solutions which depend continuously on the initial value. In order to formulate this notion of solution and to prove uniqueness in the case of a slowly growing nonlinearity, the arising energy functional is analyzed in detail.

中文翻译：

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自组织临界条件下奇异退化随机多孔介质方程的 SVI 解的适定性

我们考虑一类具有乘性 Lipschitz 连续噪声的广义随机多孔介质方程。这些方程可以与表现出自组织临界的物理模型相关。我们表明，这些 SPDE 具有独特的 SVI 解决方案，该解决方案持续依赖于初始值。为了阐述这个解的概念并证明在非线性缓慢增长的情况下的唯一性，对产生的能量泛函进行了详细分析。