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Path-by-path well-posedness of nonlinear diffusion equations with multiplicative noise
Journal de Mathématiques Pures et Appliquées ( IF 2.1 ) Pub Date : 2021-01-13 , DOI: 10.1016/j.matpur.2021.01.004
Benjamin Fehrman , Benjamin Gess

We prove the path-by-path well-posedness of stochastic porous media and fast diffusion equations driven by linear, multiplicative noise. As a consequence, we obtain the existence of a random dynamical system. This solves an open problem raised in [Barbu and Röckner (2011) [4]], [Barbu and Röckner (2018) [6]], and [Gess (2014) [11]].



中文翻译:

具乘法噪声的非线性扩散方程的逐路径适定性

我们证明了由线性,乘性噪声驱动的随机多孔介质的逐路径适定性和快速扩散方程。结果,我们获得了随机动力学系统的存在。这解决了[Barbu andRöckner(2011)[4]],[Barbu andRöckner(2018)[6]]和[Gess(2014)[11]]中提出的开放性问题。

更新日期:2021-03-02
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