Parameter identification in PDEs by the solution of monotone inclusion problems

Pankaj Gautam; Markus Grasmair

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arXiv · 2403.04557

Parameter identification in PDEs by the solution of monotone inclusion problems

Pankaj Gautam·Markus Grasmair

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Abstract

In this paper we consider the solution of monotone inverse problems using the particular example of a parameter identification problem for a semilinear parabolic PDE. For the regularized solution of this problem, we introduce a total variation based regularization method requiring the solution of a monotone inclusion problem. We show well-posedness in the sense of inverse problems of the resulting regularization scheme. In addition, we introduce and analyze a numerical algorithm for the solution of this inclusion problem using a nested inertial primal dual method. We demonstrate by means of numerical examples the convergence of both the numerical algorithm and the regularization method.

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Pankaj Gautam, Markus Grasmair. 2024-03-07. Parameter identification in PDEs by the solution of monotone inclusion problems. https://arxiv.org/abs/2403.04557

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