Some ergodic problems for Hamilton-Jacobi equations in Hilbert space
type: Item
instance of: scholarly article
title: Some ergodic problems for Hamilton-Jacobi equations in Hilbert space
zbMATH Open document ID: 0848.35026
author: Mariko Arisawa
published in: Differential and Integral Equations
publication date: 1996-02-01T00:00:00Z
review text: Existence and uniqueness results for viscosity solutions of Hamilton-Jacobi equations of the type \(H(x, \nabla u_\lambda(x))+ \lambda u_x(x)- f(x)= 0\) in \(\Omega\) with Neumann boundary conditions, where \(\Omega\) is a domain in a Hilbert space are established using Perron's method. The limit of \(\lambda u_\lambda(x)\) as \(\lambda\to \infty\) is the same constant \(d\) for each \(x\). The constant \(d\) is characterized through viscosity solutions of \(H(x, \nabla u)+ d- f(x)\leq \varepsilon\).
Mathematics Subject Classification ID: 35F30
Mathematics Subject Classification ID: 49L25
Mathematics Subject Classification ID: 35R15
zbMATH DE Number: 840301
zbMATH Keywords: Hamilton-Jacobi equations
reviewed by: Suzanne Lenhart
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 840301