Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Nonautonomous Dynamical Systems

formerly Nonautonomous and Stochastic Dynamical Systems

Editor-in-Chief: Diagana, Toka

Managing Editor: Cánovas, Jose


Mathematical Citation Quotient (MCQ) 2017: 0.71

Open Access
Online
ISSN
2353-0626
See all formats and pricing
More options …

The reconstruction of an equation of visco-elasticity

Amin Boumenir
Published Online: 2018-12-31 | DOI: https://doi.org/10.1515/msds-2018-0012

Abstract

We are concerned with the reconstruction of two coefficients of an integro-differential equation modeling the deformation of materials with memory.We show that we can explicitly reconstruct the memory, the source terms and the diffusion constant from two observations only.

References

  • [1] A. Boumenir, and A. Al-Shuaibi, The inverse Laplace transform and analytic pseudo-differential operators. J. Math. Anal. Appl. 228 (1998), no. 1, 16?36.Google Scholar

  • [2] F. Colombo, D. Guidetti, and V. Vespri, Some global in time results for integro-differential parabolic inverse problems. Differential equations: inverse and direct problems, 35-58, Lect. Notes Pure Appl. Math., 251, Chapman Hall CRC, Boca Raton, FL, 2006.CrossrefGoogle Scholar

  • [3] F. Colombo, D. Guidetti and V. Vespri, Identification of two memory kernels and the time dependence of the heat source for a parabolic conserved phase-field model. Math. Methods Appl. Sci. 28 (2005), no. 17, 2085-2115.CrossrefGoogle Scholar

  • [4] F. Colombo and V. Vespri, A semi-linear integro-differential inverse problem, Evolution equations, J. Goldstein, R. Nagel and S. Romanelli editors, Marcel Dekker, Inc., Cap 6, 234 (2003), 91-104.Google Scholar

  • [5] V.I. Krylov, and N.S. Skoblya A Handbook of Methods of Approximate Fourier Transformation and Inversion of the Laplace Transform, Mir, Moscow (1977)Google Scholar

  • [6] D.V. Widder, The Laplace Transform, Dover, 2010.Google Scholar

About the article

Received: 2018-09-27

Accepted: 2018-12-13

Published Online: 2018-12-31

Published in Print: 2018-12-01


Citation Information: Nonautonomous Dynamical Systems, Volume 5, Issue 1, Pages 152–154, ISSN (Online) 2353-0626, DOI: https://doi.org/10.1515/msds-2018-0012.

Export Citation

© by Amin Boumenir, published by De Gruyter. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

Comments (0)

Please log in or register to comment.
Log in