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

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dc.contributor.authorEsteve Yagüe, Carlos
dc.contributor.authorZuazua, Enrique
dc.date.accessioned2025-07-04T11:12:36Z
dc.date.available2025-07-04T11:12:36Z
dc.date.issued2023-02
dc.date.updated2025-07-04T11:12:36Z
dc.description.abstractWe 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.en
dc.description.sponsorshipThis project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement NO: 694126-DyCon), the Alexander von Humboldt-Professorship program, the European Unions Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 765579-ConFlex, the Transregio 154 Project “Mathematical Modelling, Simulation and Optimization Using the Example of Gas Networks”, project C08, of the German DFG, the Grant MTM2017-92996-C2-1-R COSNET of MINECO (Spain) and the Elkartek grant KK-2020/00091 CONVADP of the Basque governmenten
dc.identifier.citationEsteve-Yagüe, C., & Zuazua, E. (2023). Reachable set for Hamilton–Jacobi equations with non-smooth Hamiltonian and scalar conservation laws. Nonlinear Analysis, Theory, Methods and Applications, 227. https://doi.org/10.1016/J.NA.2022.113167
dc.identifier.doi10.1016/J.NA.2022.113167
dc.identifier.issn0362-546X
dc.identifier.urihttps://hdl.handle.net/20.500.14454/3151
dc.language.isoeng
dc.publisherElsevier Ltd
dc.rights© 2022 The Author(s)
dc.subject.otherHamilton–Jacobi equation
dc.subject.otherInverse design problem
dc.subject.otherReachable set
dc.titleReachable set for Hamilton–Jacobi equations with non-smooth Hamiltonian and scalar conservation lawsen
dc.typejournal article
dcterms.accessRightsopen access
oaire.citation.titleNonlinear Analysis, Theory, Methods and Applications
oaire.citation.volume227
oaire.licenseConditionhttps://creativecommons.org/licenses/by/4.0/
oaire.versionVoR
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