Geodesic
Optimal control for an elastic frictional contact problem
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 17 (2024) no. 2, pp. 151-161.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a mathematical model which describes a frictional contact between an elastic body and a foundation. We prove the existence of a unique weak solution to the problem. Then, we study the continuous dependence of the solution with respect to the data. Finally, we address an optimal control problem for which we prove the existence of at least one solution.
Keywords: weak solution, continuous dependence, lower semicontinuity, optimal control.
Mots-clés : Coulomb's friction 
@article{JSFU_2024_17_2_a0,
     author = {Ahlem Benraouda},
     title = {Optimal control for an elastic frictional contact problem},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {151--161},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2024_17_2_a0/}
}
TY  - JOUR
AU  - Ahlem Benraouda
TI  - Optimal control for an elastic frictional contact problem
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2024
SP  - 151
EP  - 161
VL  - 17
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2024_17_2_a0/
LA  - en
ID  - JSFU_2024_17_2_a0
ER  - 
%0 Journal Article
%A Ahlem Benraouda
%T Optimal control for an elastic frictional contact problem
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2024
%P 151-161
%V 17
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2024_17_2_a0/
%G en
%F JSFU_2024_17_2_a0
Ahlem Benraouda. Optimal control for an elastic frictional contact problem. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 17 (2024) no. 2, pp. 151-161. http://geodesic.mathdoc.fr/item/JSFU_2024_17_2_a0/

[1] C.Baiocchi, A.Capelo, Variational and Quasivariational Inequalities: Applications to Free-Boundary Problems, John Wiley, Chichester, 1984 | MR | Zbl

[2] V.Barbu, Optimal Control of Variational Inequalities, Pitman Advanced Publishing, Boston, 1984 | MR | Zbl

[3] H.Brézis, “Equations et inéquations non linéaires dans les espaces vectoriels en dualité”, Ann. Inst. Fourier (Grenoble), 18 (1968), 115–175 | DOI | MR | Zbl

[4] A.Capatina, Variational Inequalities and Frictional Contact Problems, Advances in Mechanics and Mathematics, 31, Springer, New York, 2014 | DOI | MR | Zbl

[5] A.Friedman, “Optimal control for variational inequalities”, SIAM J. Control Optim., 24:3 (1986), 439–451 | DOI | MR | Zbl

[6] W.Han, M.Sofonea, Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity, Studies in Advanced Mathematics, 30, Americal Mathematical Society, Providence, RI, 2002 | DOI | MR | Zbl

[7] I.Hlaváček, J Haslinger, J.Nečas, J.Lovíšek, Solution of Variational Inequalities in Mechanics, Springer-Verlag, New York, 1988 | MR | Zbl

[8] N.Kikuchi, J.T.Oden, “Theory of variational inequalities with applications to problems of flow through porous media”, Int. J. Engng. Sci., 18 (1980), 1173–1284 | DOI | MR | Zbl

[9] T.A.Laursen, Computational Contact and Impact Mechanics, Springer, Berlin, 2002 | MR | Zbl

[10] J.-L.Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Gauthiers-Villars, Paris, 1969 | MR

[11] R.Mignot, J.P.Puel, “Optimal control in some variational inequalities”, SIAM J. Control Optim., 22 (1984), 466–476 | DOI | MR | Zbl

[12] S.Migórski, A.Ochal, M.Sofonea, Nonlinear Inclusions and Hemivariational Inequalities. Models and Analysis of Contact Problems, Advances in Mechanics and Mathematics, 26, Springer, New York, 2013 | DOI | MR | Zbl

[13] M.Shillor, M.Sofonea, J.J.Telega, Models and Analysis of Quasistatic Contact, Lect. Notes Phys., 655, Springer, Berlin, 2004 | DOI | Zbl

[14] M.Sofonea, A.Matei, Mathematical Models in Contact Mechanics, London Mathematical Society Lecture Note Series, 398, Cambridge University Press, 2012 | Zbl

[15] M.Sofonea, S.Migórski, Variational Hemivariational Inequalities with Applications, Chapman and Hall/CRC, New York, 2017 | MR

[16] A.Touzaline, “Optimal control of a frictional contact problem”, Acta Mathematicae Applicatae Sinica, English Series, 31 (2015), 991–1000 | DOI | MR | Zbl

[17] E.Zeidler, Nonlinear Functional Analysis and its Applications, v. IV, Applications to Mathematical Physics, Springer-Verlag, New York | MR