论文标题
双线非线性随机进化方程II
Doubly nonlinear stochastic evolution equations II
论文作者
论文摘要
在[41]中补充分析，我们研究了双线性非线性类型的SPDES问题的良好性。这些是在耗散介质的建模中普遍存在的，并且对应于保守和非保守动力学之间的一般平衡法则。我们通过允许随机性扩展了经典确定性案例的范围。 Martingale解决方案的存在是通过正规化技术证明的，在最小的规律性设置中取决于Itô公式的有效性。在其他假设下，还显示了随机强大的解决方案的适合性。
Complementing the analysis in [41], we investigate the well-posedness of SPDEs problems of doubly nonlinear type. These arise ubiquitously in the modelization of dissipative media and correspond to generalized balance laws between conservative and nonconservative dynamics. We extend the reach of the classical deterministic case by allowing for stochasticity. The existence of martingale solutions is proved via a regularization technique, hinging on the validity of a Itô formula in a minimal regularity setting. Under additional assumptions, the well-posedness of stochastically strong solutions is also shown.
