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A phase field approach for optimal boundary control of damage processes in two-dimensional viscoelastic media

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In this work we investigate a phase field model for damage processes in two-dimensional viscoelastic media with non-homogeneous Neumann data describing external boundary forces. In the first part we establish global-in-time existence, uniqueness, a priori estimates and continuous dependence of strong solutions on the data. The main difficulty is caused by the irreversibility of the phase field variable which results in a constrained
PDE system. In the last part we consider an optimal control problem where a cost
functional penalizes maximal deviations from prescribed damage profiles. The goal is to minimize the cost functional with respect to exterior forces acting on the boundary which play the role of the control variable in the considered model. To this end, we prove existence of minimizers and study a family of “local” approximations via adapted cost
functionals.

Keywords: Damage processes; phase field model; viscoelasticity; nonlinear parabolic inclusions; well-posedness; optimal control.

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Informasi Detail

Judul Seri

Mathematical Models and Methods in Applied Sciences

No. Panggil

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Penerbit

: World Scientific., 2015

Deskripsi Fisik

Mathematical Models and Methods in Applied Sciences (2015)

Bahasa

English

ISBN/ISSN

DOI: 10.1142/S021820

Klasifikasi

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Tipe Isi

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Tipe Media

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Tipe Pembawa

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Edisi

(2015)

Subjek

KESEHATAN

Info Detail Spesifik

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Pernyataan Tanggungjawab

Wati/Agus

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