What is it about?

The paper deals with the reconstruction of the convolution kernel, together with the solution, in a mixed linear evolution system of hyperbolic integro‐partial differential type. This problem describes uniaxial deformations of a cylindrical domain which is filled with a linear viscoelastic solid whose material properties are supposed to be uniform on sections perpendicular to the simmetry axis. Various types of boundary conditions are prescribed. To reconstruct both the solution and the convolution kernel, we suppose of knowing for any time the flux of the viscoelastic stress vector through the lateral boundary of the cylinder.

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Why is it important?

The main novelty is that the unknown kernel is allowed to depend, not only on the time variable but also on the axial space variable.


This is a typical inverse problem, the solution of which can be applied in different fields of engineering.

Claudio Giorgi
Universita degli Studi di Brescia

Read the Original

This page is a summary of: Reconstruction of kernel depending also on space variable, Mathematical Methods in the Applied Sciences, May 2018, Wiley,
DOI: 10.1002/mma.4914.
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