Viscosity solutions for Hamilton-Jacobi equations with unbounded nonlinear term: A simplified approach
type: Item
instance of: scholarly article
title: Viscosity solutions for Hamilton-Jacobi equations with unbounded nonlinear term: A simplified approach
zbMATH Open document ID: 0810.34060
author: Daniel Tataru
published in: Journal of Differential Equations
publication date: 1994-10-10T00:00:00Z
review text: In a previous work [J. Math. Anal. Appl. 163, No. 2, 345-392 (1992; Zbl 0757.35034)] the author introduced a notion of viscosity solution for Hamilton-Jacobi equations with unbounded nonlinear term and proved existence and comparison results for both stationary problems and Cauchy problems. The purpose of the present paper is to define in a simpler and more intuitive way the class of so-called viscosity solutions for Hamilton- Jacobi equations with unbounded nonlinear term and to prove that two definitions are equivalent. The new definition seems to be closer to the approaches of M. G. Crandall and P. L. Lions and to simplify some proofs and extensions.
Mathematics Subject Classification ID: 34G20
zbMATH DE Number: 635881
zbMATH Keywords: viscosity solutions
zbMATH Keywords: Hamilton-Jacobi equations with unbounded nonlinear term
reviewed by: Maria Agostina Vivaldi
MaRDI profile type: Publication
full work available at URL: jdeq.1994.1078
OpenAlex ID: W2017229420
DOI: 10.1006/JDEQ.1994.1078
description: scientific article; zbMATH DE number 635881