An invariance principle for gradient flows in the space of probability measures
نویسندگان
چکیده
We seek to establish qualitative convergence results a general class of evolution PDEs described by gradient flows in optimal transportation distances. These come from dynamical systems under the name LaSalle Invariance Principle. By combining some basic notions flow theory and systems, we are able reproduce this invariance principle setting assumptions. apply abstract non-exhaustive list examples that recover, simplify, even extend their respective literatures.
منابع مشابه
study of cohesive devices in the textbook of english for the students of apsychology by rastegarpour
this study investigates the cohesive devices used in the textbook of english for the students of psychology. the research questions and hypotheses in the present study are based on what frequency and distribution of grammatical and lexical cohesive devices are. then, to answer the questions all grammatical and lexical cohesive devices in reading comprehension passages from 6 units of 21units th...
development and implementation of an optimized control strategy for induction machine in an electric vehicle
in the area of automotive engineering there is a tendency to more electrification of power train. in this work control of an induction machine for the application of electric vehicle is investigated. through the changing operating point of the machine, adapting the rotor magnetization current seems to be useful to increase the machines efficiency. in the literature there are many approaches wh...
15 صفحه اولExistence and Uniqueness of the Gradient Flow of the Entropy in the Space of Probability Measures
After a brief introduction on gradient flows in metric spaces and on geodesically convex functionals, we give an account of the proof (following the outline of [3, 7]) of the existence and uniqueness of the gradient flow of the Entropy in the space of Borel probability measures over a compact geodesic metric space with Ricci curvature bounded from below. Preprint SISSA 17/2014/MATE
متن کاملOptimal Control for a Mixed Flow of Hamiltonian and Gradient Type in Space of Probability Measures
Abstract. In this paper we investigate an optimal control problem in the space of measures on R. The problem is motivated by a stochastic interacting particle model which gives the 2-D Navier-Stokes equations in their vorticity formulation as mean-field equation. We prove that the associated Hamilton-Jacobi-Bellman equation, in the space of probability measures, is well-posed in an appropriatel...
متن کاملA Variational Principle for Gradient Flows of Nonconvex Energies
We present a variational approach to gradient flows of energies of the form E = φ1−φ2 where φ1, φ2 are convex functionals on a Hilbert space. A global parameter-dependent functional over trajectories is proved to admit minimizers. These minimizers converge up to subsequences to gradient-flow trajectories as the parameter tends to zero. These results apply in particular to the case of non λ-conv...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2023
ISSN: ['1090-2732', '0022-0396']
DOI: https://doi.org/10.1016/j.jde.2022.11.028