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Exploring families of energy-dissipation landscapes via tilting: three types of EDP convergence

  • This paper revolves around a subtle distinction between two concepts: passing to the limit in a family of gradient systems, on one hand, and deriving effective kinetic relations on the other. The two concepts are strongly related, and in many examples they even appear to be the same. Our main contributions are to show that they are different, to show that well-known techniques developed for the former may give incorrect results for the latter, and to introduce new tools to remedy this. The approach is based on the Energy-Dissipation Principle that provides a variational formulation to gradient-flow equations that allows one to apply techniques from Γ-convergence of functional on states and functionals on trajectories.
Author:Alexander MielkeORCiD, Alberto MontefuscoORCiD, Mark A. PeletierORCiD
Document Type:Article
Parent Title (English):Continuum Mechanics and Thermodynamics
First Page:611
Last Page:637
Publishing Institution:Zuse Institute Berlin (ZIB)
Date of first Publication:2021/01/28
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