Abstract
In this paper, we prove existence, uniqueness and regularity for a class of stochastic partial differential equations with a fractional Laplacian driven by a space-time white noise in dimension one. The equation we consider may also include a reaction term.
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Azerad, P., Mellouk, M. On a Stochastic Partial Differential Equation with Non-local Diffusion. Potential Anal 27, 183–197 (2007). https://doi.org/10.1007/s11118-007-9052-6
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DOI: https://doi.org/10.1007/s11118-007-9052-6
Keywords
- Fractional derivative operator
- Stochastic partial differential equation
- Space–time white noise
- Nonlocal diffusion
- Fourier transform