Stochastic evolution equations with nonlinear diffusivity, recent progress and critical cases
Ioana Ciotir, Dan Goreac, and Jonas M. Tölle
这篇简短的调查文章源于最近在具有添加剂,乘法或梯度噪声的变异配方中随机进化方程的关键案例的进展。 典型的例子表现为随机多孔介质方程,随机快速和超快速扩散方程,自组织临界度,随机奇异p-Laplace方程和随机总变异流等的极限案例。 我们提出了几种不同的解决方案概念,基于参数的解决方案趋同的结果,以及同质化。 此外,我们还提供了一些参考,暗示了最近在规律性结果、长期行为、人体工利和数值分析方面的进展。
This short survey article stems from recent progress on critical cases of stochastic evolution equations in variational formulation with additive, multiplicative or gradient noises. Typical examples appear as the limit cases of the stochastic porous medium equation, stochastic fast- and super fast-diffusion equations, self-organized criticality, stochastic singular p-Laplace equations, and the stochastic total variation flow, among others. We present several different notions of solutions, resul...