Some inverse problems in periodic homogenization of Hamilton-Jacobi equations

Songting Luo; Hung V. Tran; Yifeng Yu

doi:10.1007/s00205-016-0993-z

Some inverse problems in periodic homogenization of Hamilton-Jacobi equations

Analysis of PDEs 2016-04-20 v1

Authors: Songting Luo , Hung V. Tran , Yifeng Yu

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Abstract

We look at the effective Hamiltonian $\bar H$ associated with the Hamiltonian $H(p,x)=H(p)+V(x)$ in the periodic homogenization theory. Our central goal is to understand the relation between $V$ and $\bar H$ . We formulate some inverse problems concerning this relation. Such type of inverse problems are in general very challenging. In the paper, we discuss several special cases in both convex and nonconvex settings.

Keywords

periodic homogenization Hamilton-Jacobi equations effective Hamiltonian inverse problems convex settings nonconvex settings

Cite

@article{arxiv.1505.05943,
  title  = {Some inverse problems in periodic homogenization of Hamilton-Jacobi equations},
  author = {Songting Luo and Hung V. Tran and Yifeng Yu},
  journal= {arXiv preprint arXiv:1505.05943},
  year   = {2016}
}

Comments

29 pages, 5 figures

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