Asymptotic Analysis for a Class of Infinite Systems of First-Order PDE: Nonlinear Parabolic PDE in the Singular Limit

DOI10.1081/PDE-120019388zbMath1040.35128OpenAlexW2085294805MaRDI QIDQ4805329

Kazufumi Shimano, Hitoshi Ishii

Publication date: 12 May 2003

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/pde-120019388

zbMATH Keywords

existenceHamilton-Jacobi equationCauchy problemsingular limitviscosity solutionsinfinite systemperturbed test functions

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Singular perturbations in context of PDEs (35B25) Partial functional-differential equations (35R10) Initial value problems for second-order parabolic equations (35K15) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables) (35R15)

Related Items (2)

Remarks on the vanishing discount problem for infinite systems of Hamilton-Jacobi-Bellman equations ⋮ Homogenization of weakly coupled systems of Hamilton-Jacobi equations with fast switching rates

Cites Work

• Unnamed Item
• Viscosity Solutions for Weakly Coupled Systems of Hamilton-Jacobi Equations
• Periodic homogenisation of certain fully nonlinear partial differential equations
• User’s guide to viscosity solutions of second order partial differential equations
• The perturbed test function method for viscosity solutions of nonlinear PDE
• Differential equations with a small parameter and the central limit theorem for functions defined on a finite Markov chain

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