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Zeitschrift für Analysis und ihre Anwendungen


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Volume 38, Issue 3, 2019, pp. 249–286
DOI: 10.4171/ZAA/1637

Published online: 2019-07-15

Analysis of a Viscous Two-Field Gradient Damage Model I: Existence and Uniqueness

Christian Meyer[1] and Livia Mihaela Susu[2]

(1) Technische Universität Dortmund, Germany
(2) Technische Universität Dortmund, Germany

The paper deals with a viscous damage model including two damage variables, a local and a non-local one, which are coupled through a penalty term in the free energy functional. Under certain regularity conditions for linear elasticity equations, existence and uniqueness of the solution is proven, provided that the penalization parameter is chosen suciently large. Moreover, the regularity of the unique solution is investigated, in particular the di erentiability w.r.t. time.

Keywords: Viscous damage evolution, $W^{1,p}$-theory, penalization

Meyer Christian, Susu Livia Mihaela: Analysis of a Viscous Two-Field Gradient Damage Model I: Existence and Uniqueness. Z. Anal. Anwend. 38 (2019), 249-286. doi: 10.4171/ZAA/1637