Quantitative Homogenization of State-Constraint Hamilton–Jacobi Equations on Perforated Domains and Applications

We study the periodic homogenization problem of state-constraint Hamilton–Jacobi equations on perforated domains in the convex setting and obtain the optimal convergence rate. We then consider a dilute situation in which the diameter of the holes is much smaller than the microscopic scale. Finally,...

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Bibliographic Details
Published in:Archive for rational mechanics and analysis Vol. 249; no. 2; p. 18
Main Authors: Han, Yuxi, Jing, Wenjia, Mitake, Hiroyoshi, Tran, Hung V.
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2025
Springer Nature B.V
Subjects:
Careers
Classical Mechanics
Complex Systems
Constraints
Digital Object Identifier
Fluid- and Aerodynamics
Grants
Hamilton-Jacobi equation
Homogenization
Mathematical and Computational Physics
Physics
Physics and Astronomy
Telematics
Theoretical
Viscosity
ISSN:0003-9527, 1432-0673
Online Access:Get full text
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Summary:We study the periodic homogenization problem of state-constraint Hamilton–Jacobi equations on perforated domains in the convex setting and obtain the optimal convergence rate. We then consider a dilute situation in which the diameter of the holes is much smaller than the microscopic scale. Finally, a homogenization problem with domain defects where some holes are missing is analyzed.
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ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-025-02091-2