A linear algorithm for the identification of a weakly singular relaxation kernel using two boundary measurements

2016/09/26 by Sergei Avdonin, Avdonin, S., Luciano Pandolfi +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Composite Material Mechanics #FOS: Electrical engineering #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.1609.07918

openalex publication_date 2016/09/26 · openalex created_date 2016/10/07 · openalex updated_date 2026/07/28

Abstract

We consider a distributed system of a type which is encountered in the study of diffusion processes with memory and in viscoelasticity. The key feature of such system is the persistence in the future of the past actions due the memory described via a certain relaxation kernel, see below. The parameters of the kernel have to be inferred from experimental measurements. Our main result in this paper is that by using two boundary measurements the identification of a relaxation kernel which is linear combination of Abel kernels (as often assumed in applications) can be reduced to the solution of a (linear) deconvolution problem.

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