This paper establishes the global-in-time existence of a multi-phase mean curvature flow, evolving from an arbitrary closed rectifiable initial datum, which is a Brakke flow and a BV solution at the same time. In particular, we prove the validity of an explicit identity concerning the change of volume of the evolving grains, showing that their boundaries move according to the generalized mean curvature vector of the Brakke flow. Under suitable assumptions on the initial datum, such additional property resolves the non-uniqueness issue of Brakke flows.

On the existence of canonical multi-phase Brakke flows / S. Stuvard, Y. Tonegawa. - In: ADVANCES IN CALCULUS OF VARIATIONS. - ISSN 1864-8266. - (2022), pp. 1-46. [Epub ahead of print] [10.1515/acv-2021-0093]

On the existence of canonical multi-phase Brakke flows

S. Stuvard
Primo
;
2022

Abstract

This paper establishes the global-in-time existence of a multi-phase mean curvature flow, evolving from an arbitrary closed rectifiable initial datum, which is a Brakke flow and a BV solution at the same time. In particular, we prove the validity of an explicit identity concerning the change of volume of the evolving grains, showing that their boundaries move according to the generalized mean curvature vector of the Brakke flow. Under suitable assumptions on the initial datum, such additional property resolves the non-uniqueness issue of Brakke flows.
Settore MAT/05 - Analisi Matematica
23-lug-2022
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/873140
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