On a class of mixed stochastic heat equations driven by spatially homogeneous Gaussian noise. (English) Zbl 1515.60242
Summary: In this paper, we study a class of nonlinear stochastic heat equations \(\frac{\partial}{\partial t}u(t,x)=(\Delta+a^\alpha\Delta^{\frac{\alpha}{2}}+b\cdot\nabla)u(t,x)+\sigma(u(t,x))\dot{W}(t,x),\) where \(\dot{W}\) denotes the Gaussian noise which is white in time and spatially homogeneous in space. The existence, uniqueness and the Hölder continuity of the mild solution to the above equation are proved.
MSC:
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 60H07 | Stochastic calculus of variations and the Malliavin calculus |
| 60H30 | Applications of stochastic analysis (to PDEs, etc.) |
| 60G22 | Fractional processes, including fractional Brownian motion |
Keywords:
mixed stochastic heat equation; spatially homogeneous Gaussian noise; Riesz kernel; Hölder continuityReferences:
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