Homogenization of Hamilton-Jacobi Equations on Domains with Small Scale Periodic Structure

Kazuo Horie; Hitoshi Ishii

Homogenization of Hamilton-Jacobi Equations on Domains with Small Scale Periodic Structure

Kazuo Horie^*, Hitoshi Ishii

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

22 Citations (Scopus)

Abstract

We study the convergence of solutions of Hamilton-Jacobi equations on domains with small scale periodic structure as the frequency of periodicity tends to infinity. We treat both the Neumann-type and the Dirichlet boundary value problems. The limit functions are characterized as unique solutions of Hamilton-Jacobi equations with the Hamiltonians determined by the corresponding cell problems.

Original language	English
Pages (from-to)	1011-1058
Number of pages	48
Journal	Indiana University Mathematics Journal
Volume	47
Issue number	3
Publication status	Published - 1998 Sept
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)

Cite this

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abstract = "We study the convergence of solutions of Hamilton-Jacobi equations on domains with small scale periodic structure as the frequency of periodicity tends to infinity. We treat both the Neumann-type and the Dirichlet boundary value problems. The limit functions are characterized as unique solutions of Hamilton-Jacobi equations with the Hamiltonians determined by the corresponding cell problems.",

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AB - We study the convergence of solutions of Hamilton-Jacobi equations on domains with small scale periodic structure as the frequency of periodicity tends to infinity. We treat both the Neumann-type and the Dirichlet boundary value problems. The limit functions are characterized as unique solutions of Hamilton-Jacobi equations with the Hamiltonians determined by the corresponding cell problems.

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Homogenization of Hamilton-Jacobi Equations on Domains with Small Scale Periodic Structure

Abstract

ASJC Scopus subject areas

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