Nonlinear systems coupled through multi-marginal transport problems
In this paper, we introduce a dynamical urban planning model. This leads to the study of a system of nonlinear equations coupled through multi-marginal optimal transport problems. A first example consists in solving two equations coupled through the solution to the Monge–Ampère equation. We show tha...
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| Veröffentlicht in: | European journal of applied mathematics 2020-06, Vol.31 (3), p.450-469 |
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| container_title | European journal of applied mathematics |
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| creator | LABORDE, M. |
| description | In this paper, we introduce a dynamical urban planning model. This leads to the study of a system of nonlinear equations coupled through multi-marginal optimal transport problems. A first example consists in solving two equations coupled through the solution to the Monge–Ampère equation. We show that theWasserstein gradient flow theory provides a very good framework to solve these highly nonlinear systems. At the end, a uniqueness result is presented in dimension one based on convexity arguments. |
| doi_str_mv | 10.1017/S0956792519000123 |
| format | Article |
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| ispartof | European journal of applied mathematics, 2020-06, Vol.31 (3), p.450-469 |
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| language | eng |
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| source | Cambridge Journals |
| subjects | Applied mathematics Convexity Costs Flow theory Gradient flow Nonlinear equations Nonlinear systems Urban planning |
| title | Nonlinear systems coupled through multi-marginal transport problems |
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