
-
Previous Article
Existence of periodic solution for a Cahn-Hilliard/Allen-Cahn equation in two space dimensions
- EECT Home
- This Issue
-
Next Article
Asymptotic for the perturbed heavy ball system with vanishing damping term
Optimal control for a hyperbolic problem in composites with imperfect interface: A memory effect
1. | Dipartimento di Ingegneria Elettrica e dell' Informazione, Università degli Studi di Cassino e del Lazio Meridionale, via G. Di Biasio 43, Cassino, 03043, Italia |
2. | Dipartimento di Scienze e Tecnologie, Università del Sannio, Via Port' Arsa 11, Benevento, 82100, Italia |
We study an optimal control problem for certain evolution equations in two component composites with $\varepsilon$-periodic disconnected inclusions of size $\varepsilon$ in presence of a jump of the solution on the interface that varies according to a parameter $γ$. In particular the case $γ=1$ is examinated.
References:
[1] |
J. L. Auriault and H. Ene,
Macroscopic modelling of heat transfer in composites with interfacial thermal barrier, Internat. J. Heat Mass Transfer, 37 (1994), 2885-2892.
doi: 10.1016/0017-9310(94)90342-5. |
[2] |
E. Canon and J. N. Pernin,
Homogenization of diffusion in composite media with interfacial barrier, Rev. Roumaine Math. Pures Appl., 44 (1999), 23-36.
|
[3] |
D. Cioranescu and P. Donato,
Exact internal controllability in perforated domains, J. Math. Pures Appl., 68 (1989), 185-213.
|
[4] |
D. Cioranescu and P. Donato,
An Introduction to Homogenization Oxford Lecture Ser. Math., Appl., 17, Oxford University Press, New York, 1999. |
[5] |
D. Cioranescu, P. Donato and E. Zuazua,
Exact boundary controllability for the wave equation in domains with small holes, J. Math. Pures Appl., 71 (1992), 343-377.
|
[6] |
D. Cioranescu and J. Saint Jean Paulin,
Homogenization in open sets with holes, J. Math. Pures. Appl., 71 (1979), 590-607.
doi: 10.1016/0022-247X(79)90211-7. |
[7] |
U. De Maio, A. Gaudiello and C. Lefter,
Optimal Control for a Parabolic Problem in a Domain with Higly Oscillating Boundary, Appl. Anal., 83 (2004), 1245-1264.
doi: 10.1080/00036810410001724670. |
[8] |
U. De Maio, L. Faella and C. Perugia,
Optimal control problem for an anisotropic parabolic problem in a domain with very rough boundary, Ric. Mat, 63 (2014), 307-328.
doi: 10.1007/s11587-014-0183-y. |
[9] |
U. De Maio, L. Faella and C. Perugia,
Optimal control for a second-order linear evolution problem in a domain with oscillating boundary, Complex Var. Elliptic Equ., 60 (2015), 1392-1410.
doi: 10.1080/17476933.2015.1022169. |
[10] |
U. De Maio, A. K. Nandakumaran and C. Perugia,
Exact internal controllability for the wave equation in a domain with oscillating boundary with neumann boundary condition, Evol. Equ. Control Theory, 4 (2015), 325-346.
doi: 10.3934/eect.2015.4.325. |
[11] |
P. Donato,
Some corrector results for composites with imperfect interface, Rend. Mat. Appl(7), 26 (2006), 189-209.
|
[12] |
P. Donato, Homogenization of a class of imperfect transmission problems, in Multiscale Problems: Theory, Numerical Approximation and Applications, Series in Contemporary Applied
Mathematics, A. Damlamian, B. Miara and T. Li Editors, Higher Education Press, Beijing,
16 (2011), 109–147.
doi: 10.1142/9789814366892_0004. |
[13] |
P. Donato, L. Faella and S. Monsurrò,
Homogenization of the wave equation in composites with imperfect interface: A memory effect, J. Math. Pures Appl., 87 (2007), 119-143.
doi: 10.1016/j.matpur.2006.11.004. |
[14] |
P. Donato, L. Faella and S. Monsurrò,
Correctors for the homogenization of a class of hyperbolic equations with imperfect interfaces, SIAM J. Math. Anal., 40 (2009), 1952-1978.
doi: 10.1137/080712684. |
[15] |
P. Donato and E. Jose,
Corrector results for a parabolic problem with a memory effect, ESAIM: Math. Model. Numer. Anal., 44 (2010), 421-454.
doi: 10.1051/m2an/2010008. |
[16] |
P. Donato and E. Jose,
Asymptotic behavior of the approximate controls for parabolic equations with interfacial contact resistance, ESAIM: COCV, 21 (2015), 138-164.
doi: 10.1051/cocv/2014029. |
[17] |
P. Donato and S. Monsurrò,
Homogenization of two heat conductors with interfacial contact resistance, Anal. Appl., 2 (2004), 247-273.
doi: 10.1142/S0219530504000345. |
[18] |
P. Donato and A. Nabil,
Homogenization and correctors for the heat equation in perforated domains, Ricerche Mat., 50 (2001), 115-144.
|
[19] |
T. Durante, L. Faella and C. Perugia,
Homogenization and behaviour of optimal controls for the wave equation in domains with oscillating boudary, NoDEA Nonlinear Differential Equations Appl., 14 (2007), 455-489.
doi: 10.1007/s00030-007-3043-6. |
[20] |
T. Durante and T. A. Mel'nyk,
Asymptotic analysis of an optimal control problem involving a thick two-level junction with alternate type of controls, J. Optim. Th. and Appl., 144 (2010), 205-225.
doi: 10.1007/s10957-009-9604-6. |
[21] |
T. Durante and T. A. Mel'nyk,
Homogenization of quasilinear optimal control problems involving a thick multilevel junction of type 3:2:1, ESAIM: Control, Optimisation and Calculus of Variations, 18 (2012), 583-610.
doi: 10.1051/cocv/2011107. |
[22] |
L. Faella and S. Monsurr`o, Memory effects arising in the homogenization of composites with
inclusions, Topics on Mathematics for Smart System. World Sci. Publ., Hackensack, USA,
(2007), 107–121.
doi: 10.1142/9789812706874_0008. |
[23] |
L. Faella and C. Perugia,
Homogenization of a Ginzburg-Landau problem in a perforated domain with mixed boundary conditions, Bound. Value Probl, 223 (2014), 1-28.
doi: 10.1186/s13661-014-0223-2. |
[24] |
L. Faella and C. Perugia,
Optimal control for evolutionary imperfect transmission problems, Bound. Value Probl, 50 (2015), 1-16.
doi: 10.1186/s13661-015-0310-z. |
[25] |
H. C. Hummel,
Homogenization for heat transfer in polycristals with interfacial resistances, Appl. Anal., 75 (2000), 403-424.
doi: 10.1080/00036810008840857. |
[26] |
J. L. Lions,
Optimal Control of Systems Governed by Partial Differential Equations Springer-Verlag Berlin Heidelberg New York, 1971. |
[27] |
J. L. Lions,
Contràlabilité Exacte et Homogénéisation, I. Asymptotic Analysis, 1 (1988), 3-11.
|
[28] |
J. L. Lions and E. Magenes,
Non-Homogeneous Boundary Value Problems and Applications, Vol I Springer-Verlag Berlin Heidelberg New York, 1972. |
[29] |
R. Lipton,
Heat conduction in fine scale mixtures with interfacial contact resistance, SIAM J. Appl. Math., 58 (1998), 55-72.
doi: 10.1137/S0036139995295153. |
[30] |
R. Lipton and B. Vernescu,
Composite with imperfect interface, Proc. R. Soc. Lond. Ser. A, 452 (1996), 329-358.
doi: 10.1098/rspa.1996.0018. |
[31] |
S. Monsurró,
Homogenization of a two-component composite with interfacial thermal barrier, Adv. Math. Sci. Appl., 13 (2003), 43-63.
|
[32] |
S. Monsurrò,
Erratum for the paper ''Homogenization of a two-component composite with interfacial thermal barrier", Adv. Math. Sci. Appl., 14 (2004), 375-377.
|
[33] |
S. Monsurrò,
Homogenization of a composite with very small inclusions and imperfect interface. Multi scale problems and asymptotic analysis, GAKUTO Internat, Ser. Math. Sci.
Appl., Gakkotosho, Tokyo, 24 (2006), 217-232.
|
[34] |
L. Tartar, Cours Peccot, Collège de France (March 1977). Partially written in F. Murat, HConvergence, Séminaire d'analyse fonctionnelle et numérique de l'Université d'Alger (1977-78). English translation in Mathematical Modeling of Composite Materials, A. Cherkaev and R. V. Kohon ed., Progress in Nonlinear Differential Equations and their Applications,
Birkh¨auser-Verlag, (1997), 21–44. |
[35] |
E. Zeidler,
Nonlinear Functional Analysis and its Applications, Vol Ⅱ, Part A and B Springer-Verlag, New York, 1986.
doi: 10.1007/978-1-4612-4838-5. |
show all references
References:
[1] |
J. L. Auriault and H. Ene,
Macroscopic modelling of heat transfer in composites with interfacial thermal barrier, Internat. J. Heat Mass Transfer, 37 (1994), 2885-2892.
doi: 10.1016/0017-9310(94)90342-5. |
[2] |
E. Canon and J. N. Pernin,
Homogenization of diffusion in composite media with interfacial barrier, Rev. Roumaine Math. Pures Appl., 44 (1999), 23-36.
|
[3] |
D. Cioranescu and P. Donato,
Exact internal controllability in perforated domains, J. Math. Pures Appl., 68 (1989), 185-213.
|
[4] |
D. Cioranescu and P. Donato,
An Introduction to Homogenization Oxford Lecture Ser. Math., Appl., 17, Oxford University Press, New York, 1999. |
[5] |
D. Cioranescu, P. Donato and E. Zuazua,
Exact boundary controllability for the wave equation in domains with small holes, J. Math. Pures Appl., 71 (1992), 343-377.
|
[6] |
D. Cioranescu and J. Saint Jean Paulin,
Homogenization in open sets with holes, J. Math. Pures. Appl., 71 (1979), 590-607.
doi: 10.1016/0022-247X(79)90211-7. |
[7] |
U. De Maio, A. Gaudiello and C. Lefter,
Optimal Control for a Parabolic Problem in a Domain with Higly Oscillating Boundary, Appl. Anal., 83 (2004), 1245-1264.
doi: 10.1080/00036810410001724670. |
[8] |
U. De Maio, L. Faella and C. Perugia,
Optimal control problem for an anisotropic parabolic problem in a domain with very rough boundary, Ric. Mat, 63 (2014), 307-328.
doi: 10.1007/s11587-014-0183-y. |
[9] |
U. De Maio, L. Faella and C. Perugia,
Optimal control for a second-order linear evolution problem in a domain with oscillating boundary, Complex Var. Elliptic Equ., 60 (2015), 1392-1410.
doi: 10.1080/17476933.2015.1022169. |
[10] |
U. De Maio, A. K. Nandakumaran and C. Perugia,
Exact internal controllability for the wave equation in a domain with oscillating boundary with neumann boundary condition, Evol. Equ. Control Theory, 4 (2015), 325-346.
doi: 10.3934/eect.2015.4.325. |
[11] |
P. Donato,
Some corrector results for composites with imperfect interface, Rend. Mat. Appl(7), 26 (2006), 189-209.
|
[12] |
P. Donato, Homogenization of a class of imperfect transmission problems, in Multiscale Problems: Theory, Numerical Approximation and Applications, Series in Contemporary Applied
Mathematics, A. Damlamian, B. Miara and T. Li Editors, Higher Education Press, Beijing,
16 (2011), 109–147.
doi: 10.1142/9789814366892_0004. |
[13] |
P. Donato, L. Faella and S. Monsurrò,
Homogenization of the wave equation in composites with imperfect interface: A memory effect, J. Math. Pures Appl., 87 (2007), 119-143.
doi: 10.1016/j.matpur.2006.11.004. |
[14] |
P. Donato, L. Faella and S. Monsurrò,
Correctors for the homogenization of a class of hyperbolic equations with imperfect interfaces, SIAM J. Math. Anal., 40 (2009), 1952-1978.
doi: 10.1137/080712684. |
[15] |
P. Donato and E. Jose,
Corrector results for a parabolic problem with a memory effect, ESAIM: Math. Model. Numer. Anal., 44 (2010), 421-454.
doi: 10.1051/m2an/2010008. |
[16] |
P. Donato and E. Jose,
Asymptotic behavior of the approximate controls for parabolic equations with interfacial contact resistance, ESAIM: COCV, 21 (2015), 138-164.
doi: 10.1051/cocv/2014029. |
[17] |
P. Donato and S. Monsurrò,
Homogenization of two heat conductors with interfacial contact resistance, Anal. Appl., 2 (2004), 247-273.
doi: 10.1142/S0219530504000345. |
[18] |
P. Donato and A. Nabil,
Homogenization and correctors for the heat equation in perforated domains, Ricerche Mat., 50 (2001), 115-144.
|
[19] |
T. Durante, L. Faella and C. Perugia,
Homogenization and behaviour of optimal controls for the wave equation in domains with oscillating boudary, NoDEA Nonlinear Differential Equations Appl., 14 (2007), 455-489.
doi: 10.1007/s00030-007-3043-6. |
[20] |
T. Durante and T. A. Mel'nyk,
Asymptotic analysis of an optimal control problem involving a thick two-level junction with alternate type of controls, J. Optim. Th. and Appl., 144 (2010), 205-225.
doi: 10.1007/s10957-009-9604-6. |
[21] |
T. Durante and T. A. Mel'nyk,
Homogenization of quasilinear optimal control problems involving a thick multilevel junction of type 3:2:1, ESAIM: Control, Optimisation and Calculus of Variations, 18 (2012), 583-610.
doi: 10.1051/cocv/2011107. |
[22] |
L. Faella and S. Monsurr`o, Memory effects arising in the homogenization of composites with
inclusions, Topics on Mathematics for Smart System. World Sci. Publ., Hackensack, USA,
(2007), 107–121.
doi: 10.1142/9789812706874_0008. |
[23] |
L. Faella and C. Perugia,
Homogenization of a Ginzburg-Landau problem in a perforated domain with mixed boundary conditions, Bound. Value Probl, 223 (2014), 1-28.
doi: 10.1186/s13661-014-0223-2. |
[24] |
L. Faella and C. Perugia,
Optimal control for evolutionary imperfect transmission problems, Bound. Value Probl, 50 (2015), 1-16.
doi: 10.1186/s13661-015-0310-z. |
[25] |
H. C. Hummel,
Homogenization for heat transfer in polycristals with interfacial resistances, Appl. Anal., 75 (2000), 403-424.
doi: 10.1080/00036810008840857. |
[26] |
J. L. Lions,
Optimal Control of Systems Governed by Partial Differential Equations Springer-Verlag Berlin Heidelberg New York, 1971. |
[27] |
J. L. Lions,
Contràlabilité Exacte et Homogénéisation, I. Asymptotic Analysis, 1 (1988), 3-11.
|
[28] |
J. L. Lions and E. Magenes,
Non-Homogeneous Boundary Value Problems and Applications, Vol I Springer-Verlag Berlin Heidelberg New York, 1972. |
[29] |
R. Lipton,
Heat conduction in fine scale mixtures with interfacial contact resistance, SIAM J. Appl. Math., 58 (1998), 55-72.
doi: 10.1137/S0036139995295153. |
[30] |
R. Lipton and B. Vernescu,
Composite with imperfect interface, Proc. R. Soc. Lond. Ser. A, 452 (1996), 329-358.
doi: 10.1098/rspa.1996.0018. |
[31] |
S. Monsurró,
Homogenization of a two-component composite with interfacial thermal barrier, Adv. Math. Sci. Appl., 13 (2003), 43-63.
|
[32] |
S. Monsurrò,
Erratum for the paper ''Homogenization of a two-component composite with interfacial thermal barrier", Adv. Math. Sci. Appl., 14 (2004), 375-377.
|
[33] |
S. Monsurrò,
Homogenization of a composite with very small inclusions and imperfect interface. Multi scale problems and asymptotic analysis, GAKUTO Internat, Ser. Math. Sci.
Appl., Gakkotosho, Tokyo, 24 (2006), 217-232.
|
[34] |
L. Tartar, Cours Peccot, Collège de France (March 1977). Partially written in F. Murat, HConvergence, Séminaire d'analyse fonctionnelle et numérique de l'Université d'Alger (1977-78). English translation in Mathematical Modeling of Composite Materials, A. Cherkaev and R. V. Kohon ed., Progress in Nonlinear Differential Equations and their Applications,
Birkh¨auser-Verlag, (1997), 21–44. |
[35] |
E. Zeidler,
Nonlinear Functional Analysis and its Applications, Vol Ⅱ, Part A and B Springer-Verlag, New York, 1986.
doi: 10.1007/978-1-4612-4838-5. |

[1] |
Leszek Gasiński, Nikolaos S. Papageorgiou. Relaxation of optimal control problems driven by nonlinear evolution equations. Evolution Equations and Control Theory, 2020, 9 (4) : 1027-1040. doi: 10.3934/eect.2020050 |
[2] |
Erik Kropat. Homogenization of optimal control problems on curvilinear networks with a periodic microstructure --Results on $\boldsymbol{S}$-homogenization and $\boldsymbol{Γ}$-convergence. Numerical Algebra, Control and Optimization, 2017, 7 (1) : 51-76. doi: 10.3934/naco.2017003 |
[3] |
Kim Dang Phung, Gengsheng Wang, Xu Zhang. On the existence of time optimal controls for linear evolution equations. Discrete and Continuous Dynamical Systems - B, 2007, 8 (4) : 925-941. doi: 10.3934/dcdsb.2007.8.925 |
[4] |
Ulisse Stefanelli, Daniel Wachsmuth, Gerd Wachsmuth. Optimal control of a rate-independent evolution equation via viscous regularization. Discrete and Continuous Dynamical Systems - S, 2017, 10 (6) : 1467-1485. doi: 10.3934/dcdss.2017076 |
[5] |
Gengsheng Wang, Guojie Zheng. The optimal control to restore the periodic property of a linear evolution system with small perturbation. Discrete and Continuous Dynamical Systems - B, 2010, 14 (4) : 1621-1639. doi: 10.3934/dcdsb.2010.14.1621 |
[6] |
Elimhan N. Mahmudov. Optimal control of evolution differential inclusions with polynomial linear differential operators. Evolution Equations and Control Theory, 2019, 8 (3) : 603-619. doi: 10.3934/eect.2019028 |
[7] |
Leszek Gasiński. Optimal control problem of Bolza-type for evolution hemivariational inequality. Conference Publications, 2003, 2003 (Special) : 320-326. doi: 10.3934/proc.2003.2003.320 |
[8] |
Norbert Koksch, Stefan Siegmund. Feedback control via inertial manifolds for nonautonomous evolution equations. Communications on Pure and Applied Analysis, 2011, 10 (3) : 917-936. doi: 10.3934/cpaa.2011.10.917 |
[9] |
Urszula Ledzewicz, Stanislaw Walczak. Optimal control of systems governed by some elliptic equations. Discrete and Continuous Dynamical Systems, 1999, 5 (2) : 279-290. doi: 10.3934/dcds.1999.5.279 |
[10] |
Eduardo Casas, Konstantinos Chrysafinos. Analysis and optimal control of some quasilinear parabolic equations. Mathematical Control and Related Fields, 2018, 8 (3&4) : 607-623. doi: 10.3934/mcrf.2018025 |
[11] |
Y. Efendiev, B. Popov. On homogenization of nonlinear hyperbolic equations. Communications on Pure and Applied Analysis, 2005, 4 (2) : 295-309. doi: 10.3934/cpaa.2005.4.295 |
[12] |
Elimhan N. Mahmudov. Infimal convolution and duality in convex optimal control problems with second order evolution differential inclusions. Evolution Equations and Control Theory, 2021, 10 (1) : 37-59. doi: 10.3934/eect.2020051 |
[13] |
Elimhan N. Mahmudov. Optimal control of Sturm-Liouville type evolution differential inclusions with endpoint constraints. Journal of Industrial and Management Optimization, 2020, 16 (5) : 2503-2520. doi: 10.3934/jimo.2019066 |
[14] |
Ștefana-Lucia Aniţa. Optimal control for stochastic differential equations and related Kolmogorov equations. Evolution Equations and Control Theory, 2022 doi: 10.3934/eect.2022023 |
[15] |
Hakima Bessaih, Yalchin Efendiev, Florin Maris. Homogenization of the evolution Stokes equation in a perforated domain with a stochastic Fourier boundary condition. Networks and Heterogeneous Media, 2015, 10 (2) : 343-367. doi: 10.3934/nhm.2015.10.343 |
[16] |
Gabriella Zecca. An optimal control problem for some nonlinear elliptic equations with unbounded coefficients. Discrete and Continuous Dynamical Systems - B, 2019, 24 (3) : 1393-1409. doi: 10.3934/dcdsb.2019021 |
[17] |
Lucas Bonifacius, Ira Neitzel. Second order optimality conditions for optimal control of quasilinear parabolic equations. Mathematical Control and Related Fields, 2018, 8 (1) : 1-34. doi: 10.3934/mcrf.2018001 |
[18] |
Peng Zhong, Suzanne Lenhart. Study on the order of events in optimal control of a harvesting problem modeled by integrodifference equations. Evolution Equations and Control Theory, 2013, 2 (4) : 749-769. doi: 10.3934/eect.2013.2.749 |
[19] |
Ping Lin, Weihan Wang. Optimal control problems for some ordinary differential equations with behavior of blowup or quenching. Mathematical Control and Related Fields, 2018, 8 (3&4) : 809-828. doi: 10.3934/mcrf.2018036 |
[20] |
Shu Luan. On the existence of optimal control for semilinear elliptic equations with nonlinear neumann boundary conditions. Mathematical Control and Related Fields, 2017, 7 (3) : 493-506. doi: 10.3934/mcrf.2017018 |
2021 Impact Factor: 1.169
Tools
Metrics
Other articles
by authors
[Back to Top]