Abstract
We establish a class of stochastic partial differential equations (SPDEs) driven by space-time fractional noises, where we suppose that the drift term contains a gradient and satisfies certain non-Lipschitz condition. We prove the strong existence and uniqueness and joint Hölder continuity of the solution to the SPDEs.
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Acknowledgements
This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 11571190, 11771218, 11771018, 12061004), the Natural Science Foundation of Ningxia (No. 2020AAC03230), and the Major Research Project for North Minzu University (No. ZDZX201902).
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Jiang, Y., Yang, X. Stochastic partial differential equations with gradient driven by space-time fractional noises. Front. Math. China 16, 479–497 (2021). https://doi.org/10.1007/s11464-021-0875-z
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DOI: https://doi.org/10.1007/s11464-021-0875-z
Keywords
- Stochastic partial differential equation (SPDE)
- fractional noise
- uniqueness
- strong solution
- Hölder continuity