The defining equation $(\ast):\ \dot \omega_t=-F'(\omega_t),$ of a gradient flow is kinetic in essence. This article explores some dynamical (rather than kinetic) features of gradient flows (i) by embedding equation $(\ast)$ into the family of slowed down gradient flow equations: $\dot \omega ^{ \varepsilon}_t=- \varepsilon F'( \omega ^{ \varepsilon}_t),$ where $\varepsilon>0$, and (ii) by considering the \emph{accelerations} $\ddot \omega ^{ \varepsilon}_t$. We shall focus on Wasserstein gradient flows. Our approach is mainly heuristic. It relies on Otto calculus.A special formulation of the Schrödinger problem consists in minimizing some action on the Wasserstein space of probability measures on a Riemannian manifold subject to fixe...
This is the first of a series of papers devoted to a thorough analysis of the class of gradient flow...
Abstract. We give a new proof of the contraction in the Wasserstein dis-tance for the semigroup defi...
The gradient flow of the Canham-Helfrich functional is tackled via the Generalized Minimizing Moveme...
International audienceThe defining equation $(\ast):\ \dot \omega_t=-F'(\omega_t),$ of a gradient f...
We propose a generalization of the Schr\"odinger problem by replacing the usual entropy with a funct...
Many evolutionary partial differential equations may be rewritten as the gradient flow of an energy ...
A recurring obstacle in the study of Wasserstein gradient flow is the lack of convexity of...
We develop the long-time analysis for gradient flow equations in metric spaces. In particular, we co...
Starting from a motivation in the modeling of crowd movement, the paper presents the topics of gradi...
Gradient flows of energy functionals on the space of probability measures with Wasserstein metric ha...
In this work, we study the Wasserstein gradient flow of the Riesz energy defined on the space of pro...
In this work, we study the Wasserstein gradient flow of the Riesz energy defined on the space of pro...
An algebraic decay rate is derived which bounds the time required for velocities to equilibrate in a...
In this paper, we characterize a degenerate PDE as the gradient flow in the space of nonnegative mea...
A wide range of diffusion equations can be interpreted as gradient flow with respect to Wasserstein ...
This is the first of a series of papers devoted to a thorough analysis of the class of gradient flow...
Abstract. We give a new proof of the contraction in the Wasserstein dis-tance for the semigroup defi...
The gradient flow of the Canham-Helfrich functional is tackled via the Generalized Minimizing Moveme...
International audienceThe defining equation $(\ast):\ \dot \omega_t=-F'(\omega_t),$ of a gradient f...
We propose a generalization of the Schr\"odinger problem by replacing the usual entropy with a funct...
Many evolutionary partial differential equations may be rewritten as the gradient flow of an energy ...
A recurring obstacle in the study of Wasserstein gradient flow is the lack of convexity of...
We develop the long-time analysis for gradient flow equations in metric spaces. In particular, we co...
Starting from a motivation in the modeling of crowd movement, the paper presents the topics of gradi...
Gradient flows of energy functionals on the space of probability measures with Wasserstein metric ha...
In this work, we study the Wasserstein gradient flow of the Riesz energy defined on the space of pro...
In this work, we study the Wasserstein gradient flow of the Riesz energy defined on the space of pro...
An algebraic decay rate is derived which bounds the time required for velocities to equilibrate in a...
In this paper, we characterize a degenerate PDE as the gradient flow in the space of nonnegative mea...
A wide range of diffusion equations can be interpreted as gradient flow with respect to Wasserstein ...
This is the first of a series of papers devoted to a thorough analysis of the class of gradient flow...
Abstract. We give a new proof of the contraction in the Wasserstein dis-tance for the semigroup defi...
The gradient flow of the Canham-Helfrich functional is tackled via the Generalized Minimizing Moveme...