Semi-local classification of geometric singularities for Hamilton-Jacobi equations
type: Item
instance of: scholarly article
title: Semi-local classification of geometric singularities for Hamilton-Jacobi equations
zbMATH Open document ID: 0837.35091
published in: Journal of Differential Equations
publication date: 1995-07-05T00:00:00Z
review text: The authors consider the Cauchy problem for Hamilton-Jacobi equations and study the generation and propagation of singularities appearing in the solutions. To consider this problem, the first author [Adv. Stud. Pure Math. 22, 89-100 (1993; reviewed above)] defined a notion of ``geometric solution'' in a framework of one parameter Legendrian unfoldings. On the other hand, the theory of viscosity solutions assured the global existence of weak solutions which satisfy the supplementary condition. Singularities of viscosity solutions correspond to the intersection of branches of a graph of multivalued geometric solutions. The principal part of this paper is as follows: To study the bifurcation of the branches of its graph, they formulated the problem in terms of multi- Legendrian unfoldings and gave the generic list of the bifurcations of the branches of the multivalued graph. The construction of singularities of weak solutions is not mentioned here. But they announce to publish a paper on this subject.
Mathematics Subject Classification ID: 35L67
Mathematics Subject Classification ID: 35F25
Mathematics Subject Classification ID: 58C25
Mathematics Subject Classification ID: 58K99
Mathematics Subject Classification ID: 76L05
zbMATH DE Number: 759465
zbMATH Keywords: Hamilton-Jacobi equations
zbMATH Keywords: viscosity solutions
zbMATH Keywords: geometric solutions
zbMATH Keywords: multi-Legendrian unfoldings
author: Shyuichi Izumiya
author: Georgios T. Kossioris
reviewed by: Mikio Tsuji
MaRDI profile type: Publication
OpenAlex ID: W2076070598
DOI: 10.1006/JDEQ.1995.1071
Recommended article: Semi-concave singularities and the Hamilton-Jacobi equation
Recommended article: Q4281132
Recommended article: Realization theorems of geometric singularities for Hamilton-Jacobi equations
Recommended article: Singularities of solutions of time dependent Hamilton-Jacobi equations. Applications to Riemannian geometry
Recommended article: On the topology of the set of singularities of a solution to the Hamilton-Jacobi equation
Recommended article: Singularities of solutions of Hamilton-Jacobi equations
Recommended article: Q3749485
Recommended article: Algebraic aspects of classification of singularities in Hamiltonian systems
Recommended article: Classification of hyperbolic singularities of rank zero of integrable Hamiltonian systems
Recommended article: Global propagation of singularities for solutions of Hamilton-Jacobi equations
description: scientific article; zbMATH DE number 759465