Weak differentiability of the control-to-state mapping in a parabolic equation with hysteresis
Analysis of PDEs
2019-05-07 v1
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.
Keywords
Cite
@article{arxiv.1905.01863,
title = {Weak differentiability of the control-to-state mapping in a parabolic equation with hysteresis},
author = {Martin Brokate and Klemens Fellner and Matthias Lang-Batsching},
journal= {arXiv preprint arXiv:1905.01863},
year = {2019}
}