On inverse source problems for space-dependent sources in thermoelasticity. (English) Zbl 07919538
Chatzakou, Marianna (ed.) et al., Modern problems in PDEs and applications. Extended abstracts of the 2023 GAP Center summer school, Ghent, Belgium, August 23 – September 2, 2023. Cham: Birkhäuser. Trends Math., Res. Perspect. Ghent Anal. PDE Cent. 4, 153-161 (2024).
Summary: The aim of this contribution is to discuss the results in Maes and Van Bockstal (J Inverse Ill-Posed Prob (5)4, 2022). These uniqueness results deal with inverse source problems of determining a space-dependent load or heat source in thermoelastic systems. The additional measurements are taken to be the final in time or time-average measurement of the displacement and/or time-average measurements of the temperature.
For the entire collection see [Zbl 1541.35005].
For the entire collection see [Zbl 1541.35005].
MSC:
| 74F05 | Thermal effects in solid mechanics |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
| 35A15 | Variational methods applied to PDEs |
| 35R30 | Inverse problems for PDEs |
References:
| [1] | Alphonse, A., Rautenberg, C.N., Rodrigues, J.F.: Analysis of a quasi-variational contact problem arising in thermoelasticity. Nonlinear Anal. 217, 112728 (2022) · Zbl 1509.35301 |
| [2] | Bellassoued, M., Yamamoto, M.: Carleman estimates and an inverse heat source problem for the thermoelasticity system. Inverse Probl. 27(1), ID 015006 (2011) · Zbl 1208.35167 |
| [3] | Biot, M.A.: Thermoelasticity and irreversible thermodynamics. J. Appl. Phys. 27(3), 240-253 (1956) · Zbl 0071.41204 |
| [4] | Chandrasekharaiah, D.S.: Thermoelasticity with second sound: a review. Appl. Mech. Rev. 39(3), 355-376 (1986) · Zbl 0588.73006 |
| [5] | Demir, M.H., Yigit, F.: Thermoelastic stability analysis of solidification of pure metals on a coated planar mold of finite thickness. Metall. Mat. Trans. B 48(2), 966-982 (2017) |
| [6] | Maes, F., Van Bockstal, K.: Thermoelastic problem in the setting of dual-phase-lag heat conduction: Existence and uniqueness of a weak solution. J. Math. Anal. Appl. 503(1) 125304 (2021) · Zbl 1509.74016 |
| [7] | Maes, F., Van Bockstal, K.: Uniqueness for inverse source problems of determining a space-dependent source in thermoelastic systems. J. Inverse Ill-Posed Probl. 5(4), 1-12 (2022) |
| [8] | Mak, A.F., Zhang, M., Boone, D.A.: State-of-the-art research in lower-limb prosthetic biomechanics-socket interface: A review. J. Rehabil. Res. Dev. 38(2), 161-174 (2001) |
| [9] | Muñoz Rivera, J.E., Qin, Y.: Global existence and exponential stability in one-dimensional nonlinear thermoelasticity with thermal memory. Nonlinear Anal. 51(1), 11-32 (2002) · Zbl 1057.74008 |
| [10] | Nohel, J.A., Shea, D.F.: Frequency domain methods for Volterra equations. Adv. Math. 22(3), 278-304 (1976) · Zbl 0349.45004 |
| [11] | Tönük, E., Silver-Thorn, M.B.: Nonlinear elastic material property estimation of lower extremity residual limb tissues. IEEE Trans. Neural Syst. Rehabil. Eng. 11(1), 43-53 (2003) |
| [12] | Van Bockstal, K.: Inverse source problems in thermoelasticity. In: Ruzhanksy, M., Torebek, B. (eds.) Extended Abstracts MWCAPDE 2023. Birkhäuser, Cham (2024). https://link.springer.com/book/9783031416644 |
| [13] | Van Bockstal, K., Marin, L.: Recovery of a space-dependent vector source in anisotropic thermoelastic systems. Comput. Methods Appl. Mech. Eng. 321, 269-293 (2017) · Zbl 1439.74102 |
| [14] | Van Bockstal, K., Marin, L.: Finite element method for the reconstruction of a time-dependent heat source in isotropic thermoelasticity systems of type-III. Z. Angew. Math. Phys. 73(3), 27 (2022) · Zbl 1490.74113 |
| [15] | Van Bockstal, K., Slodička, M.: Recovery of a space-dependent vector source in thermoelastic systems. Inverse Probl. Sci. Eng. 23(6), 956-968 (2015) · Zbl 1329.65214 |
| [16] | Van Bockstal, K., Slodička, M.: Recovery of a time-dependent heat source in one-dimensional thermoelasticity of type-III. Inverse Probl. Sci. Eng. 25(5), 749-770 (2017) · Zbl 1369.74023 |
| [17] | Warby, M.K., Whiteman, J.R., Jiang, W.-G., Warwick, P., Wright, T.: Finite element simulation of thermoforming processes for polymer sheets. Math. Comput. Simul. 61(3-6), 209-218 (2003) · Zbl 1011.82504 |
| [18] | Wu, B., Liu, J.: Determination of an unknown source for a thermoelastic system with a memory effect. Inverse Prob. 28(9), ID 095012 (2012) · Zbl 1250.35189 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
