Abstract
In this paper, we investigate the non-autonomous Hamilton-Jacobi equation
where H is 1-periodic with respect to t and M is a compact Riemannian manifold without boundary. We obtain the viscosity solution denoted by \(T_{{t_0}}^t\phi (x)\) and show \(T_{{t_0}}^t\phi (x)\) converges uniformly to a time-periodic viscosity solution u* (x, t) of ∂tu + H(t, x, ∂xu, u) = 0.
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Acknowledgements
The first author was supported by National Natural Science Foundation of China (Grant Nos. 11801223 and 11871267). The second author was supported by National Natural Science Foundation of China (Grant No. 11501437) and the China Post-doctoral Science Foundation (Grant No. 2017M611439). The third author was supported by National Natural Science Foundation of China (Grant Nos. 11631006 and 11790272) and Shanghai Science and Technology Commission (Grant No. 17XD1400500).
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Chen, C., Wang, YN. & Yan, J. Convergence of the viscosity solution of non-autonomous Hamilton-Jacobi equations. Sci. China Math. 64, 1789–1800 (2021). https://doi.org/10.1007/s11425-019-1631-0
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DOI: https://doi.org/10.1007/s11425-019-1631-0