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arXiv · 1905.01863

Weak differentiability of the control-to-state mapping in a parabolic equation with hysteresis

Martin Brokate·Klemens Fellner·Matthias Lang-Batsching
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Abstract

We consider the heat equation on a bounded domain subject to an inhomogeneous forcing in terms of a rate-independent (hysteresis) operator and a control variable. The aim of the paper is to establish a functional analytical setting which allows to prove weak differentiability properties of the control-to-state mapping. Using results of [BK] and [B] on the weak differentiability of scalar rate-independent operators, we prove Bouligand and Newton differentiability in suitable Bochner spaces of the control-to-state mapping in a parabolic problem.

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Martin Brokate, Klemens Fellner, Matthias Lang-Batsching. 2019-05-06. Weak differentiability of the control-to-state mapping in a parabolic equation with hysteresis. https://arxiv.org/abs/1905.01863

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