Proceedings of the Japan Academy, Series A, Mathematical Sciences

Existence result for a doubly degenerate quasilinear stochastic parabolic equation

Mamadou Sango

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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.

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Proc. Japan Acad. Ser. A Math. Sci., Volume 81, Number 5 (2005), 89-94.

First available in Project Euclid: 3 June 2005

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Zentralblatt MATH identifier

Primary: 60H15: Stochastic partial differential equations [See also 35R60] 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15]

Doubly degenerate stochastic parabolic equations splitting-up method compactness


Sango, Mamadou. Existence result for a doubly degenerate quasilinear stochastic parabolic equation. Proc. Japan Acad. Ser. A Math. Sci. 81 (2005), no. 5, 89--94. doi:10.3792/pjaa.81.89.

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