Repository: Freie Universität Berlin, Math Department

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

Mielke, Alexander and Montefusco, Alberto and Peletier, Mark A. (2021) Exploring families of energy-dissipation landscapes via tilting: three types of EDP convergence. Continuum Mechanics and Thermodynamics, 33 (2). pp. 611-637.

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Abstract We introduce two new concepts of convergence of gradient systems (Q, Eε,Rε) to a limiting gradient system (Q, E0,R0). These new concepts are called ‘EDP convergence with tilting’ and ‘contact–EDP convergencewith tilting.’ Both are based on the energy-dissipation-principle (EDP) formulation of solutions of gradient systems and can be seen as refinements of the Gamma-convergence for gradient flows first introduced by Sandier and Serfaty. The two newconcepts are constructed in order to avoid the ‘unnatural’ limiting gradient structures that sometimes arise as limits in EDP convergence. EDP convergence with tilting is a strengthening of EDP convergence by requiring EDP convergence for a full family of ‘tilted’ copies of (Q, Eε,Rε). It avoids unnatural limiting gradient structures, but many interesting systems are non-convergent according to this concept. Contact–EDP convergence with tilting is a relaxation of EDP convergence with tilting and still avoids unnatural limits but applies to a broader class of sequences (Q, Eε,Rε). In this paper, we define these concepts, study their properties, and connect them with classical EDP convergence.We illustrate the different concepts on a number of test problems. Continuum Mech. Thermodyn. (2021) 33:611–637

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:2657
Deposited By: Monika Drueck
Deposited On:17 Jan 2022 14:48
Last Modified:17 Jan 2022 14:48

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