Wave fronts for Hamilton-Jacobi equations: The general theory for Riemann solutions in \(\mathbb{R}^n\)
type: Item
instance of: scholarly article
title: Wave fronts for Hamilton-Jacobi equations: The general theory for Riemann solutions in \(\mathbb{R}^n\)
zbMATH Open document ID: 0923.70015
author: F. M. Tangerman
author: James Glimm
author: Herbert C. Kranzer
author: Dechun Tan
published in: Communications in Mathematical Physics
publication date: 1998-02-25T00:00:00Z
review text: The authors consider a class of 1-homogeneous Hamiltonian functions \(H(p)\) and weak solutions, that is, Crandall-Evans-Lions viscosity solutions, for the Hamilton-Jacobi equation \(S_t+H(S_x)=0\) on the space-time \(\mathbb{R}^n\times\mathbb{R}^+\). The authors point out that propagation and bifurcation of discontinuities of such solutions can be studied by means of associated Riemann problems. Furthermore, they investigate those Riemann solutions forming an elementary wave pattern, thus generalizing the notion of shock waves and centered rarefaction waves of one-dimensional conservations laws. Among other things, there is an interesting remark about an application of Hamilton-Jacobi equations (different from the usual ones, like optics) to the manufacture of semiconductor chips.
Mathematics Subject Classification ID: 70H20
zbMATH DE Number: 1121172
zbMATH Keywords: 1-homogeneous Hamiltonian functions
zbMATH Keywords: weak solutions
zbMATH Keywords: Crandall-Evans-Lions viscosity solutions
zbMATH Keywords: wave pattern
zbMATH Keywords: shock waves
zbMATH Keywords: centered rarefaction waves
zbMATH Keywords: one-dimensional conservations laws
zbMATH Keywords: manufacture of semiconductor chips
reviewed by: Franco Cardin
MaRDI profile type: Publication
full work available at URL: s002200050153
OpenAlex ID: W2008656693
DOI: 10.1007/S002200050153
description: scientific article; zbMATH DE number 1121172