Reachable set for Hamilton-Jacobi equations with non-smooth Hamiltonian and scalar conservation laws

Esteve-Yague C, Zuazua Iriondo E (2023)

Publication Language: English

Publication Status: Accepted

Publication Type: Journal article, Original article

Future Publication Type: Journal article

Publication year: 2023

Journal

Nonlinear Analysis: Hybrid Systems Elsevier BV

Publisher: Nonlinear Analysis

Book Volume: 227

Journal Issue: 113167

URI: https://dcn.nat.fau.eu/wp-content/uploads/reachableHamiltonJacobi-cEsteveY-eZuazua-2203.04731.pdf

DOI: 10.1016/j.na.2022.113167

Open Access Link: https://dcn.nat.fau.eu/wp-content/uploads/reachableHamiltonJacobi-cEsteveY-eZuazua-2203.04731.pdf

Abstract

We give a full characterization of the range of the operator which associates, to any initial condition, the viscosity solution at time T of a Hamilton-Jacobi equation with convex Hamiltonian. Our main motivation is to be able to treat the case of convex Hamiltonians with no further regularity assumptions. We give special attention to the case H(p)=|p|, for which we provide a rather geometrical description of the range of the viscosity operator by means of an interior ball condition on the sublevel sets. From our characterization of the reachable set, we are able to deduce further results concerning, for instance, sharp regularity estimates for the reachable functions, as well as structural properties of the reachable set. The results are finally adapted to the case of scalar conservation laws in dimension one.

Authors with CRIS profile

Enrique Zuazua Iriondo Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Additional Organisation(s)

Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Involved external institutions

University of Cambridge GB United Kingdom (GB)

How to cite

APA:

Esteve-Yague, C., & Zuazua Iriondo, E. (2023). Reachable set for Hamilton-Jacobi equations with non-smooth Hamiltonian and scalar conservation laws. Nonlinear Analysis: Hybrid Systems, 227(113167). https://doi.org/10.1016/j.na.2022.113167

MLA:

Esteve-Yague, Carlos, and Enrique Zuazua Iriondo. "Reachable set for Hamilton-Jacobi equations with non-smooth Hamiltonian and scalar conservation laws." Nonlinear Analysis: Hybrid Systems 227.113167 (2023).

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