论文标题
具有非线性梯度噪声和Dirichlet边界条件的多孔介质方程
Porous media equations with nonlinear gradient noise and Dirichlet boundary conditions
论文作者
论文摘要
在完整的（0，\ infty）$的全部状态$ m \中，我们建立了用于多孔介质和具有非线性梯度噪声的快速扩散方程的解决方案以及任何初始数据。此外，如果初始数据是正数据，则解决方案是唯一的。反过来，这些方程的解决方案图是驱动噪声的连续函数，它会生成相关的随机动力学系统。最后，在\ {1 \} \ cup（2，\ infty）$的制度$ m \中，上述所有结果也适用于签名的初始数据。
We establish pathwise existence of solutions for porous media and fast diffusion equations with nonlinear gradient noise, in the full regime $m\in(0,\infty)$ and for any initial data in $L^2$. Moreover, if the initial data is positive, solutions are pathwise unique. In turn, the solution map of these equations is a continuous function of the driving noise and it generates an associated random dynamical system. Finally, in the regime $m\in\{1\}\cup(2,\infty)$, all the aforementioned results also hold for signed initial data.
