The tangential cone condition for some coefficient identification model problems in parabolic PDEs

TL;DR

This paper verifies the tangential cone condition for specific time-dependent inverse problems in parabolic PDEs, aiding the convergence analysis of iterative solution methods for these ill-posed problems.

Contribution

It introduces a series of benchmark inverse problems in parabolic PDEs where the tangential cone condition can be explicitly verified.

Findings

Verified the tangential cone condition for multiple inverse problems

Provided benchmarks for future convergence analysis

Enhanced understanding of iterative methods in parabolic PDEs

Abstract

The tangential condition was introduced in [Hanke et al., 95] as a sufficient condition for convergence of the Landweber iteration for solving ill-posed problems. In this paper we present a series of time dependent benchmark inverse problems for which we can verify this condition.