Some Inverse Problems in Periodic Homogenization of Hamilton-Jacobi Equations

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• 作者：Songting Luo ; Hung V. Tran ; Yifeng Yu
• 刊名：Archive for Rational Mechanics and Analysis
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：221
• 期：3
• 页码：1585-1617
• 全文大小：782 KB
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mechanics
  Electromagnetism, Optics and Lasers
  Mathematical and Computational Physics
  Complexity
  Fluids
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0673
• 卷排序：221

文摘

We look at the effective Hamiltonian \({\overline{H}}\) 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 \({\overline{H}}\). We formulate some inverse problems concerning this relation. Such types of inverse problems are, in general, very challenging. In this paper, we discuss several special cases in both convex and nonconvex settings.Communicated by W. EThe work of SL is partially supported by NSF Grant DMS-1418908, the work of HT is partially supported by NSF Grants DMS-1361236 and DMS-1615944, and the work of YY is partially supported by NSF CAREER award #1151919.