Joint identification via deconvolution of the flux and energy relaxation kernels of the Gurtin-Pipkin model in thermodynamics with memory

TL;DR

This paper introduces a linear deconvolution-based method to identify energy and flux relaxation kernels in Gurtin-Pipkin thermodynamics models, enabling kernel reconstruction from experimental measurements.

Contribution

It proposes a novel linear approach that reduces kernel identification to solving two deconvolution problems, improving accuracy and efficiency.

Findings

Energy kernel reconstructed via energy measurements.

Flux kernel identified using flux measurements.

Method simplifies kernel identification process.

Abstract

In this paper we present a linear method for the identification of both the energy and flux relaxation kernels in the equation of thermodynamics with memory proposed by M.E. Gurtin and A.G. Pipkin. The method reduces the identification of the two kernels to the solution of two (linear) deconvolution problems. The energy relaxation kernel is reconstructed by means of energy measurements as the solution of a Volterra integral equation of the first kind which does not depend on the still unknown flux relaxation kernel. Then, flux measurements are used to identify the flux relaxation kernel.