论文标题
SVI解决方案对单数取代的随机多孔培养基方程的适应性良好
Well-posedness of SVI solutions to singular-degenerate stochastic porous media equations arising in self-organised criticality
论文作者
论文摘要
我们考虑一类具有多重Lipschitz连续噪声的广义随机多孔介质方程。这些方程可能与表现出自组织批判性的物理模型有关。我们表明，这些SPDE具有独特的SVI解决方案，这些解决方案不断取决于初始值。为了制定解决方案的概念并在缓慢增长的非线性的情况下证明了独特性，详细分析了产生的能量功能。
We consider a class of generalised stochastic porous media equations with multiplicative Lipschitz continuous noise. These equations can be related to physical models exhibiting self-organised 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 analysed in detail.
