Initial value problems viewed as generalized optimal transport problems with matrix-valued density fields

Speaker: Yann Brenier

Date: Fri, Jan 29, 2021

Location: Zoom

Conference: PIHOT kick-off event

Subject: Mathematics, Partial Differential Equations

Class: Scientific

CRG: Pacific Interdisciplinary Hub on Optimal Transport (2021-2024)

Abstract:

The initial value problem for many important PDEs (Burgers, Euler, Hamilton-Jacobi, Navier-Stokes equations, systems of conservation laws with convex entropy, etc…) can be often reduced to a convex minimization problem that can be seen as a generalized optimal transport problem involving matrix-valued density fields. The time boundary conditions enjoy a backward-forward structure of “ballistic” type, just as in mean-field game theory.

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