Abstract
In this paper, we establish a large deviation principle for the solutions to the stochastic heat equations with logarithmic nonlinearity driven by Brownian motion, which is neither locally Lipschitz nor locally monotone. Nonlinear versions of Gronwall’s inequalities and Log-Sobolev inequalities play an important role.
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Acknowledgements
The authors would like to thank the anonymous referees and the editor for their constructive comments that improved the quality of this paper. This work is partially supported by the National Key R &D Program of China (No. 2022YFA1006001), the National Natural Science Foundation of China (No. 12131019, No. 12001516, No. 11721101), the Fundamental Research Funds for the Central Universities (No. WK3470000031, No. WK0010000081, No. WK3470000024).
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Pan, T., Shang, S. & Zhang, T. Large Deviations of Stochastic Heat Equations with Logarithmic Nonlinearity. Potential Anal (2024). https://doi.org/10.1007/s11118-024-10142-8
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DOI: https://doi.org/10.1007/s11118-024-10142-8
Keywords
- Stochastic partial differential equations
- Logarithmic nonlinearity
- Large deviation principle
- Weak convergence method