A general convergence result for viscosity solutions of Hamilton-Jacobi equations and non-linear semigroups

Kraaij, R.C.

doi:10.1016/j.jfa.2021.109346

A general convergence result for viscosity solutions of Hamilton-Jacobi equations and non-linear semigroups

Title

A general convergence result for viscosity solutions of Hamilton-Jacobi equations and non-linear semigroups

Author

Kraaij, R.C. (TU Delft Applied Probability)

Date

2022-03-01

Abstract

We extend the Barles-Perthame procedure [4] (see also [22]) of semi-relaxed limits of viscosity solutions of Hamilton-Jacobi equations of the type f−λHf=h to the context of non-compact spaces. The convergence result allows for equations on a ‘converging sequence of spaces’ as well as Hamilton-equations written in terms of two equations in terms of operators H_† and H_‡ that serve as natural upper and lower bounds for the ‘true’ operator H. In the process, we establish a strong relation between non-linear pseudo-resolvents and viscosity solutions of Hamilton-Jacobi equations. As a consequence we derive a convergence result for non-linear semigroups.

Subject

Barles-Perthame method
Hamilton-Jacobi equation
Non-linear semigroups
Viscosity solutions

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http://resolver.tudelft.nl/uuid:54c0a3f7-621b-4504-893b-9b02307c19f7

DOI

https://doi.org/10.1016/j.jfa.2021.109346

ISSN

0022-1236

Source

Journal of Functional Analysis, 282 (5)

Part of collection

Institutional Repository