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Large time average of reachable sets and Applications to Homogenization of interfaces moving with oscillatory spatio-temporal velocity

Wenjia Jing Yau Mathematical Sciences Center, Tsinghua University, No 1. Tsinghua Yuan, Beijing 100084, China Panagiotis E. Souganidis Department of Mathematics, The University of Chicago, 5734 S. University Ave., Chicago, IL 60637, USA Hung V. Tran Department of Mathematics, University of Wisconsin at Madison, 480 Lincoln Drive, Madison, WI 53706, USA

Analysis of PDEs Optimization and Control Probability mathscidoc:2206.03012

Discrete and Continuous Dynamical Systems - S, 11, (5), 915-939, 2018.10
We study the averaging of fronts moving with positive oscillatory normal velocity, which is periodic in space and stationary ergodic in time. The problem can be formulated as the homogenization of coercive level set Hamilton-Jacobi equations with spatio-temporal oscillations. To overcome the difficulties due to the oscillations in time and the linear growth of the Hamiltonian, we first study the long time averaged behavior of the associated reachable sets using geometric arguments. The results are new for higher than one dimensions even in the space-time periodic setting.
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@inproceedings{wenjia2018large,
  title={Large time average of reachable sets and Applications to Homogenization of interfaces moving with oscillatory spatio-temporal velocity},
  author={Wenjia Jing, Panagiotis E. Souganidis, and Hung V. Tran},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220626164849483624465},
  booktitle={Discrete and Continuous Dynamical Systems - S},
  volume={11},
  number={5},
  pages={915-939},
  year={2018},
}
Wenjia Jing, Panagiotis E. Souganidis, and Hung V. Tran. Large time average of reachable sets and Applications to Homogenization of interfaces moving with oscillatory spatio-temporal velocity. 2018. Vol. 11. In Discrete and Continuous Dynamical Systems - S. pp.915-939. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220626164849483624465.
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