Nonlinear inclusion for thermo-electro-elastic: existence, dependence and optimal control

[1] S. Adly and T. Haddad, An implicit sweeping process approach to quasistatic evolution variational inequalities, SIAM J. Math. Anal. 50 (2018), no. 1, 761–778.
https://doi.org/10.1137/17M1120658

[2] S. Adly and M. Sofonea, Time-dependent inclusions and sweeping processes in contact mechanics, Z. fur Angew. Math. Phys. 70 (2019), no. 2, Article number: 39
https://doi.org/10.1007/s00033-019-1084-4

[3] O. Baiz, H. Benaissa, R. Bouchantouf, and D. El Moutawakil, Optimization problems for a thermoelastic frictional contact problem, Math. Model. Anal. 26 (2021), no. 3, 444–468.
https://doi.org/10.3846/mma.2021.12803

[4] O. Baiz, H. Benaissa, D. El Moutawakil, and R. Fakhar, Variational and numerical analysis of a quasistatic thermo-electro-visco-elastic frictional contact problem, ZAMM. J. Appl. Math. Mech. 99 (2019), no. 3, Article ID: e201800138.
https://doi.org/10.1002/zamm.201800138

[5] O. Baiz, H. Benaissa, Z. Faiz, and D. El Moutawakil, Variational-hemivariational inverse problem for electro-elastic unilateral frictional contact problem, J. Inverse Ill-Posed Probl. 29 (2021), no. 6, 917–934.
https://doi.org/10.1515/jiip-2020-0051

[6] H. Benaissa, El-H. Essoufi, and R. Fakhar, Existence results for unilateral contact problem with friction of thermoelectro-elasticity, Appl. Math. Mech. 36 (2015), no. 7, 911—-926.
https://doi.org/10.1007/s10483-015-1957-9

[7] H. Benaissa, El-H. Essoufi, and R. Fakhar, Variational analysis of a thermo-piezoelectric contact problem with friction, Jour. Adv. Res. Appl. Math. 7 (2015), no. 2, 52–75.

[8] R. Bouchantouf, O. Baiz, D. El Moutawakil, and H. Benaissa, Optimal control of a frictional thermo-piezoelectric contact problem, Int. J. Dynam. Control 11 (2023), no. 2, 821–834.
https://doi.org/10.1007/s40435-022-01019-y

[9] A. Capatina, Optimal control of a signorini contact problem, Numer. Funct. Anal. Optim. 21 (2000), no. 7-8, 817–828.
https://doi.org/10.1080/01630560008816987

[10] T. Chen, R. Hu, and M. Sofonea, Analysis and control of an electro-elastic contact problem, Math. Mech. Solids 27 (2022), no. 5, 813–827.
https://doi.org/10.1177/10812865211044181

[11] Z. Denkowski, S. Migórski, and A. Ochal, Optimal control for a class of mechanical thermoviscoelastic frictional contact problems, Control Cybernet. 36 (2007), no. 3, 611–632.

[12] Z. Faiz, O. Baiz, H. Benaissa, and D. El Moutawakil, Analysis and approximation of hemivariational inequality for a frictional thermo-electro-visco-elastic contact problem with damage, Taiwanese J. Math. 27 (2023), no. 1, 81–111.
https://doi.org/10.11650/tjm/220704

[13] A. Matei and S. Micu, Boundary optimal control for nonlinear antiplane problems, Nonlinear Anal. Theory Methods Appl. 74 (2011), no. 5, 1641–1652.
https://doi.org/10.1016/j.na.2010.10.034

[14] A. Matei and S. Micu, Boundary optimal control for a frictional contact problem with normal compliance, Appl. Math. Optim. 78 (2018), no. 2, 379–401.
https://doi.org/10.1007/s00245-017-9410-8

[15] S. Migórski, A. Ochal, and M. Sofonea, Nonlinear Inclusions and Hemivariational Inequalities: Models and Analysis of Contact Problems, vol. 26, Springer Science & Business Media, New York, 2012.

[16] S. Migórski and P. Szafraniec, A class of dynamic frictional contact problems governed by a system of hemivariational inequalities in thermoviscoelasticity, Non-linear Anal. Real World Appl. 15 (2014), 158–171.
https://doi.org/10.1016/j.nonrwa.2013.07.002

[17] F. Nacry and M. Sofonea, A class of nonlinear inclusions and sweeping processes in solid mechanics, Acta Appl. Math. 171 (2021), no. 1, Article number: 16
https://doi.org/10.1007/s10440-020-00380-4

[18] F. Nacry and M. Sofonea, History-dependent operators and prox-regular sweeping processes, Fixed Point Theory Algorithms Sci. Eng. 2022 (2022), no. 1, Article number: 5
https://doi.org/10.1186/s13663-022-00715-w

[19] F. Nacry and M. Sofonea, A history-dependent sweeping processes in contact mechanics, J. Convex Anal. 29 (2022), no. 1, 77–100.

[20] M. Sofonea, Optimal control of a class of variational–hemivariational inequalities in reflexive banach spaces, Appl. Math. Optim. 79 (2019), no. 3, 621–646.
https://doi.org/10.1007/s00245-017-9450-0

[21] M. Sofonea, Analysis and control of stationary inclusions in contact mechanics, Non-linear Anal. Real World Appl. 61 (2021), Article ID: 103335.
https://doi.org/10.1016/j.nonrwa.2021.103335

[22] M. Sofonea and A. Matei, Mathematical Models in Contact Mechanics, vol. 398, Cambridge University Press., 2012.

[23] M. Sofonea and S. Migorski, Variational-Hemivariational Inequalities with Applications, CRC Press, New York, 2017.

[24] P. Szafraniec, Dynamic nonsmooth frictional contact problems with damage in thermoviscoelasticity, Math. Mech. Solids 21 (2016), no. 5, 525–538.
https://doi.org/10.1177/1081286514527860

[25] P. Szafraniec, Analysis of an elasto-piezoelectric system of hemivariational inequalities with thermal effects, Acta Math. Sci. 37 (2017), no. 4, 1048–1060.
https://doi.org/10.1016/S0252-9602(17)30057-7