Generalized viscosity solutions for Hamilton-Jacobi equations with time- measurable Hamiltonians
type: Item
instance of: scholarly article
title: Generalized viscosity solutions for Hamilton-Jacobi equations with time- measurable Hamiltonians
zbMATH Open document ID: 0632.35008
DOI: 10.1016/0022-0396(87)90183-5
published in: Journal of Differential Equations
publication date: 1987-01-01T00:00:00Z
review text: This paper extends the definition of viscosity solution to nonlinear first order Hamilton-Jacobi equations, \(u_ t+H(t,x,D_ xu)=0\), with time-measurable Hamiltonians, and derives a corresponding uniqueness result. The proof uses the ``blow up'' method, which removes the dependence of the Hamiltonian on (x,t). The discussion of ``blow up'' method is of substantial independent interest. The extended definition involves restricting the class of test functions used in the standard definition of viscosity solutions.
Mathematics Subject Classification ID: 35F30
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 4027971
zbMATH Keywords: viscosity solution
zbMATH Keywords: first order
zbMATH Keywords: Hamilton-Jacobi equations
zbMATH Keywords: time- measurable Hamiltonians
zbMATH Keywords: uniqueness
zbMATH Keywords: blow up
author: Emmanuel N. Barron
author: Robert R. Jensen
MaRDI profile type: Publication
full work available at URL: 0022-0396(87)90183-5
OpenAlex ID: W2062515792
cites work: The Pontryagin Maximum Principle From Dynamic Programming and Viscosity Solutions to First-Order Partial Differential Equations
cites work: Viscosity solutions of Isaacs' equations and differential games with Lipschitz controls
cites work: Viscosity Solutions of Hamilton-Jacobi Equations
cites work: Some Properties of Viscosity Solutions of Hamilton-Jacobi Equations
cites work: Differential games and nonlinear first order PDE on bounded domains
cites work: Q3396313
cites work: Q4942594
cites work: Remarks on Hamilton-Jacobi equations with measurable time-dependent Hamiltonians
cites work: Asymptotic behavior of some nonlinear heat equations
description: scientific article; zbMATH DE number 4027971