Identification of the relaxation kernel in diffusion processes and viscoelasticity with memory via deconvolution

TL;DR

This paper introduces a linear deconvolution algorithm to identify the relaxation kernel in diffusion and viscoelastic systems by observing boundary flux, enabling better understanding of memory effects in these materials.

Contribution

The paper proposes a novel linear Volterra integral equation-based method for kernel identification from boundary flux observations in diffusion and viscoelasticity.

Findings

Effective algorithm for relaxation kernel identification

Applicable to diffusion and viscoelastic systems with memory

Improves understanding of boundary flux measurements

Abstract

We present an algorithm for the identification of the relaxation kernel in the theory of diffusion systems with memory (or of viscoelasticity) which is linear, in the sense that we propose a linear Volterra integral equation of convolution type whose solution is the relaxation kernel. The algorithm is based on the observation of the flux through a part of the boundary of a body.