Some Inverse Problems in Periodic Homogenization of Hamilton-Jacobi Equations

We look at the effective Hamiltonian 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 H ¯ . We formulate some inverse problems concerning this relation. Such types of inverse proble...

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Bibliographic Details
Published in:Archive for rational mechanics and analysis 2016-09, Vol.221 (3), p.1585-1617
Main Authors: Luo, Songting, Tran, Hung V., Yu, Yifeng
Format: Article
Language:English
Subjects:
Archives
Classical Mechanics
Complex Systems
Fluid- and Aerodynamics
Formulas (mathematics)
Hamilton-Jacobi equation
Homogenization
Homogenizing
Inverse problems
Mathematical and Computational Physics
Physics
Physics and Astronomy
Texts
Theoretical
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Summary:We look at the effective Hamiltonian 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 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.
ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-016-0993-z