Discontinuous solutions in L ∞ for Hamilton-Jacobi equations
An approach is introduced to construct global discontinuous solutions in L ∞ for Hamilton-Jacobi equations. This approach allows the initial data only in L ∞ and applies to the equations with nonconvex Hamiltonians. The profit functions are introduced to formulate the notion of discontinuous solutio...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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Kluwer Academic Publishers
2000
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| _version_ | 1826295274743529472 |
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| author | Guiqiang, C Bo, S |
| author_facet | Guiqiang, C Bo, S |
| author_sort | Guiqiang, C |
| collection | OXFORD |
| description | An approach is introduced to construct global discontinuous solutions in L ∞ for Hamilton-Jacobi equations. This approach allows the initial data only in L ∞ and applies to the equations with nonconvex Hamiltonians. The profit functions are introduced to formulate the notion of discontinuous solutions in L ∞. The existence of global discontinuous solutions in L ∞ is established. These solutions in L ∞ coincide with the viscosity solutions and the minimax solutions, provided that the initial data are continuous. A prototypical equation is analyzed to examine the L ∞ stability of our L ∞ solutions. The analysis also shows that global discontinuous solutions are determined by the topology in which the initial data are approximated. © 1983 Shanghai Scientific and Technological Literature Publishing House. |
| first_indexed | 2024-03-07T03:58:31Z |
| format | Journal article |
| id | oxford-uuid:c3b3b7dc-c273-4a1c-aa9d-3ddc5587fa8d |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T03:58:31Z |
| publishDate | 2000 |
| publisher | Kluwer Academic Publishers |
| record_format | dspace |
| spelling | oxford-uuid:c3b3b7dc-c273-4a1c-aa9d-3ddc5587fa8d2022-03-27T06:18:23ZDiscontinuous solutions in L ∞ for Hamilton-Jacobi equationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:c3b3b7dc-c273-4a1c-aa9d-3ddc5587fa8dEnglishSymplectic Elements at OxfordKluwer Academic Publishers2000Guiqiang, CBo, SAn approach is introduced to construct global discontinuous solutions in L ∞ for Hamilton-Jacobi equations. This approach allows the initial data only in L ∞ and applies to the equations with nonconvex Hamiltonians. The profit functions are introduced to formulate the notion of discontinuous solutions in L ∞. The existence of global discontinuous solutions in L ∞ is established. These solutions in L ∞ coincide with the viscosity solutions and the minimax solutions, provided that the initial data are continuous. A prototypical equation is analyzed to examine the L ∞ stability of our L ∞ solutions. The analysis also shows that global discontinuous solutions are determined by the topology in which the initial data are approximated. © 1983 Shanghai Scientific and Technological Literature Publishing House. |
| spellingShingle | Guiqiang, C Bo, S Discontinuous solutions in L ∞ for Hamilton-Jacobi equations |
| title | Discontinuous solutions in L ∞ for Hamilton-Jacobi equations |
| title_full | Discontinuous solutions in L ∞ for Hamilton-Jacobi equations |
| title_fullStr | Discontinuous solutions in L ∞ for Hamilton-Jacobi equations |
| title_full_unstemmed | Discontinuous solutions in L ∞ for Hamilton-Jacobi equations |
| title_short | Discontinuous solutions in L ∞ for Hamilton-Jacobi equations |
| title_sort | discontinuous solutions in l ∞ for hamilton jacobi equations |
| work_keys_str_mv | AT guiqiangc discontinuoussolutionsinlforhamiltonjacobiequations AT bos discontinuoussolutionsinlforhamiltonjacobiequations |