Existence result for a doubly degenerate quasilinear stochastic parabolic equation

Abstract

Using the splitting-up method, we establish a new existence result for an initial boundary value problem for the doubly degenerate stochastic quasilinear parabolic equation \begin{equation*} d \bigl( \left|y\right|^{\alpha-2}y\bigr) -\left[ \sum_{i=1}^{n} \frac{\partial}{\partial x_{i}} \left( \left| \frac{\partial y}{\partial x}\right|^{p-2} \frac{\partial y}{\partial x_{i}}\right) - g(t,y) \right] dt = \sum_{l=0}^{d}h_{l} (t,y) dW_{t}^{l}, \end{equation*} where $W_{t}^{l}$ are one-dimensional Wiener process defined on a complete probability space, $p$, $\alpha$ and the functions $g$ and $h_{l}$ satisfy appropriate restrictions.