The Lax solution to a Hamilton-Jacobi equation and its generalizations: Part 2

Ya V. Mykytiuk; A. K. Prykarpatsky; D. Blackmore

doi:10.1016/j.na.2003.08.004

The Lax solution to a Hamilton-Jacobi equation and its generalizations: Part 2

Ya V. Mykytiuk, A. K. Prykarpatsky, D. Blackmore

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

A study on the Lax solution to a Hamilton-Jacobi equation is presented. It is proved that the function defined by the infimum-based Lax formula provides a solution almost everywhere in x for each fixed t>0 to the Hamilton-Jacobi, Cauchy problem. A generalization of the Lax formula is developed for the more inclusive Hamilton-Jacobi equation.

Original language	English (US)
Pages (from-to)	629-640
Number of pages	12
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	55
Issue number	5
DOIs	https://doi.org/10.1016/j.na.2003.08.004
State	Published - Nov 2003

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

Keywords

F set
Hamilton-Jacobi equation
Lax formula
Lebesgue measure
Semicontinuity
Viscosity solution

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10.1016/j.na.2003.08.004

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abstract = "A study on the Lax solution to a Hamilton-Jacobi equation is presented. It is proved that the function defined by the infimum-based Lax formula provides a solution almost everywhere in x for each fixed t>0 to the Hamilton-Jacobi, Cauchy problem. A generalization of the Lax formula is developed for the more inclusive Hamilton-Jacobi equation.",

keywords = "F set, Hamilton-Jacobi equation, Lax formula, Lebesgue measure, Semicontinuity, Viscosity solution",

author = "Mykytiuk, {Ya V.} and Prykarpatsky, {A. K.} and D. Blackmore",

year = "2003",

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AU - Mykytiuk, Ya V.

AU - Prykarpatsky, A. K.

AU - Blackmore, D.

PY - 2003/11

Y1 - 2003/11

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AB - A study on the Lax solution to a Hamilton-Jacobi equation is presented. It is proved that the function defined by the infimum-based Lax formula provides a solution almost everywhere in x for each fixed t>0 to the Hamilton-Jacobi, Cauchy problem. A generalization of the Lax formula is developed for the more inclusive Hamilton-Jacobi equation.

KW - F set

KW - Hamilton-Jacobi equation

KW - Lax formula

KW - Lebesgue measure

KW - Semicontinuity

KW - Viscosity solution

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JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 5

ER -

The Lax solution to a Hamilton-Jacobi equation and its generalizations: Part 2

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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