Interpreting systems of continuity equations in spaces of probability measures through PDE duality
We introduce a notion of duality solution for a single or a system of transport equations in spaces of probability measures reminiscent of the viscosity solution notion for nonlinear parabolic equations. Our notion of solution by duality is, under suitable assumptions, equivalent to gradient flow so...
| Główni autorzy: | , |
|---|---|
| Format: | Journal article |
| Język: | English |
| Wydane: |
Springer
2024
|
| _version_ | 1826313467802419200 |
|---|---|
| author | Carrillo, JA Gómez-Castro, D |
| author_facet | Carrillo, JA Gómez-Castro, D |
| author_sort | Carrillo, JA |
| collection | OXFORD |
| description | We introduce a notion of duality solution for a single or a system of transport equations in spaces of probability measures reminiscent of the viscosity solution notion for nonlinear parabolic equations. Our notion of solution by duality is, under suitable assumptions, equivalent to gradient flow solutions in case the single/system of equations has this structure. In contrast, we can deal with a quite general system of nonlinear non-local, diffusive or not, system of PDEs without any variational structure. |
| first_indexed | 2024-09-25T04:13:53Z |
| format | Journal article |
| id | oxford-uuid:68b536b8-e06d-4733-8eae-f4fe0f42fadb |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-09-25T04:13:53Z |
| publishDate | 2024 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:68b536b8-e06d-4733-8eae-f4fe0f42fadb2024-07-15T07:50:32ZInterpreting systems of continuity equations in spaces of probability measures through PDE dualityJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:68b536b8-e06d-4733-8eae-f4fe0f42fadbEnglishSymplectic ElementsSpringer2024Carrillo, JAGómez-Castro, DWe introduce a notion of duality solution for a single or a system of transport equations in spaces of probability measures reminiscent of the viscosity solution notion for nonlinear parabolic equations. Our notion of solution by duality is, under suitable assumptions, equivalent to gradient flow solutions in case the single/system of equations has this structure. In contrast, we can deal with a quite general system of nonlinear non-local, diffusive or not, system of PDEs without any variational structure. |
| spellingShingle | Carrillo, JA Gómez-Castro, D Interpreting systems of continuity equations in spaces of probability measures through PDE duality |
| title | Interpreting systems of continuity equations in spaces of probability measures through PDE duality |
| title_full | Interpreting systems of continuity equations in spaces of probability measures through PDE duality |
| title_fullStr | Interpreting systems of continuity equations in spaces of probability measures through PDE duality |
| title_full_unstemmed | Interpreting systems of continuity equations in spaces of probability measures through PDE duality |
| title_short | Interpreting systems of continuity equations in spaces of probability measures through PDE duality |
| title_sort | interpreting systems of continuity equations in spaces of probability measures through pde duality |
| work_keys_str_mv | AT carrilloja interpretingsystemsofcontinuityequationsinspacesofprobabilitymeasuresthroughpdeduality AT gomezcastrod interpretingsystemsofcontinuityequationsinspacesofprobabilitymeasuresthroughpdeduality |