Stability of the determination of a time-dependent coefficient in parabolic equations

Mourad Choulli; Yavar Kian

Stability of the determination of a time-dependent coefficient in parabolic equations

Analysis of PDEs 2016-02-01 v1

Authors: Mourad Choulli , Yavar Kian

Abstract

We establish a Lipschitz stability estimate for the inverse problem consisting in the determination of the coefficient $\sigma(t)$ , appearing in a Dirichlet initial-boundary value problem for the parabolic equation $\partial_tu-\Delta_x u+\sigma(t)f(x)u=0$ , from Neumann boundary data. We extend this result to the same inverse problem when the previous linear parabolic equation in changed to the semi-linear parabolic equation $\partial_tu-\Delta_x u=F(t,x,\sigma(t),u(x,t))$ .

Keywords

inverse problems parabolic equations time-dependent coefficient Lipschitz stability Neumann boundary data semi-linear parabolic equations

Cite

@article{arxiv.1202.5392,
  title  = {Stability of the determination of a time-dependent coefficient in parabolic equations},
  author = {Mourad Choulli and Yavar Kian},
  journal= {arXiv preprint arXiv:1202.5392},
  year   = {2016}
}

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