A new family of transportation costs with applications to reaction-diffusion and parabolic equations with boundary conditions

摘要

This paper introduces a family of transportation costs between non-negative measures. This family is used to obtain parabolic and reaction-diffusion equations with drift, subject to Dirichlet boundary condition, as the gradient flow of the entropy functional integral(Omega) rho log rho + V rho + 1 dx. In [1], Figalli and Gigli study a transportation cost that can be used to obtain parabolic equations with drift subject to Dirichlet boundary condition. However, the drift and the boundary condition are coupled in that work. The costs in this paper allow the drift and the boundary condition to be detached. (C) 2018 Elsevier Masson SAS. All rights reserved.