An integrable example of gradient flow based on optimal transport of differential forms
| Autor: | Yann Brenier, Xianglong Duan |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Integrable system
Euclidean space Differential form Applied Mathematics 010102 general mathematics Mathematical analysis Eulerian path 01 natural sciences Parabolic partial differential equation 010101 applied mathematics symbols.namesake symbols Heat equation Uniqueness 0101 mathematics Balanced flow Analysis Mathematics |
| Zdroj: | Calculus of Variations and Partial Differential Equations. 57 |
| ISSN: | 1432-0835 0944-2669 |
| DOI: | 10.1007/s00526-018-1370-6 |
| Popis: | Optimal transport theory has been a powerful tool for the analysis of parabolic equations viewed as gradient flows of volume forms according to suitable transportation metrics. In this paper, we present an example of gradient flows for closed (d-1)-forms in the Euclidean space R^d. In spite of its apparent complexity, the resulting very degenerate parabolic system is fully integrable and can be viewed as the Eulerian version of the heat equation for curves in the Euclidean space. We analyze this system in terms of ``relative entropy" and ``dissipative solutions" and provide global existence and weak-strong uniqueness results. |
| Databáze: | OpenAIRE |
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