Open Access
Issue |
ESAIM: COCV
Volume 27, 2021
|
|
---|---|---|
Article Number | 100 | |
Number of page(s) | 28 | |
DOI | https://doi.org/10.1051/cocv/2021088 | |
Published online | 21 October 2021 |
- A. Abdulle and T.N. Pouchon, A priori error analysis of the finite element heterogeneous multiscale method for the wave equation in heterogeneous media over long time. SIAM J. Numer. Anal. 54 (2016) 1507–1534. [CrossRef] [MathSciNet] [Google Scholar]
- A. Abdulle and T.N. Pouchon, Effective models for the multidimensional wave equation in heterogeneous media over long time and numerical homogenization. Math. Models Methods Appl. Sci. 26 (2016). [Google Scholar]
- A. Abdulle and T.N. Pouchon, Effective models and numerical homogenization for wave propagation in heterogeneous media on arbitrary timescales. Found. Comput. Math. 20 (2020) 1505–1547. [CrossRef] [MathSciNet] [Google Scholar]
- G. Allaire, M. Briane and M. Vanninathan, A comparison between two scale asymptotic expansions and Bloch wave expansions for the homogenization of periodic structures. SEMA J. 73 (2016) 237–259. [CrossRef] [MathSciNet] [Google Scholar]
- G. Allaire, A. Lamacz-Keymling and J. Rauch, Crime pays; homogenized wave equations for long times. To appear Asymptotic Analysis. [Google Scholar]
- N. Bakhvalov and G. Panasenko, Homogenization: Averaging Processes in Periodic Media. Kluwer, Dordrecht (1989). [CrossRef] [Google Scholar]
- A. Benoit and A. Gloria, Long-time homogenization and asymptotic ballistic transport of classical waves. Annales Scientifiques de l’École Normale Supérieure 52 (2019) 703–759. [CrossRef] [MathSciNet] [Google Scholar]
- A. Bensoussan, J.-L. Lions and G. Papanicolaou, Asymptotic analysis for periodic structures. Corrected reprint ofthe 1978 original, AMS Chelsea Publishing, Providence, RI (2011). [Google Scholar]
- G. Bouchitté and B. Schweizer, Homogenization of Maxwell’s equations in a split ring geometry. Multiscale Model. Simul. 8 (2010) 717–750. [CrossRef] [MathSciNet] [Google Scholar]
- S. Brahim-Otsmane, G.A. Francfort and F. Murat, Correctors for the homogenization of the wave and heat equations. J. Math. Pures Appl. 71 (1992) 197–231. [MathSciNet] [Google Scholar]
- G. Buttazzo, M.E. Drakhlin, L. Freddi and E. Stepanov, Homogenization of optimal control problems for functional-differential equations. J. Optim. Theory Appl. 93 (1997) 103–119. [CrossRef] [MathSciNet] [Google Scholar]
- D. Cioranescu, A. Damlamian, P. Donato, G. Griso and R. Zaki, The periodic unfolding method in domains with holes. SIAM J. Math. Anal. 44 (2012) 718–760. [CrossRef] [MathSciNet] [Google Scholar]
- C. Conca and M. Vanninathan, Homogenization of periodic structures via Bloch decomposition. SIAM J. Appl. Math. 57 (1997) 1639–1659. [CrossRef] [MathSciNet] [Google Scholar]
- C. Conca, R. Orive and M. Vanninathan, Bloch approximation in homogenization and applications. SIAM J. Math. Anal. 33 (2002) 1166–1198. [CrossRef] [MathSciNet] [Google Scholar]
- C. Conca, R. Orive and M. Vanninathan, On Burnett coefficients in periodic media. J. Math. Phys. 47 (2006) 032902. [CrossRef] [MathSciNet] [Google Scholar]
- U. De Maio, P. Kogut and R. Manzo, Asymptotic analysis of an optimal boundary control problem for ill-posed elliptic equation in domains with rugous boundary. Asymptot. Anal. 118 (2020) 209–234. [MathSciNet] [Google Scholar]
- T. Dohnal, A. Lamacz and B. Schweizer, Bloch-wave homogenization on large time scales and dispersive effective wave equations. Multiscale Model. Simul. 12 (2014) 488–513. [CrossRef] [MathSciNet] [Google Scholar]
- T. Dohnal, A. Lamacz and B. Schweizer, Dispersive homogenized models and coefficient formulas for waves in general periodic media. Asymptot. Anal. 93 (2015) 21–49. [MathSciNet] [Google Scholar]
- S. Kesavan and T. Muthukumar, Homogenization of an optimal control problem with state-constraints. Differ. Equ. Dyn. Syst. 19 (2011) 361–374. [CrossRef] [MathSciNet] [Google Scholar]
- S. Kesavan and M. Rajesh, Homogenization of periodic optimal control problems via multi-scale convergence. Proc. Indian Acad. Sci. Math. Sci. 108 (1998) 189–207. [CrossRef] [MathSciNet] [Google Scholar]
- S. Kesavan and J. Saint Jean Paulin, Homogenization of an optimal control problem. SIAM J. Control Optim. 35 (1997) 1557–1573. [CrossRef] [MathSciNet] [Google Scholar]
- P. Kogut, Higher-order asymptotics of the solutions of the problem of the optimal control of a distributed system with rapidly oscillating coefficients. Ukrainian Math. J. 48 (1996) 1063–1073. [CrossRef] [MathSciNet] [Google Scholar]
- P. Kogut and G. Leugering, Homogenization of optimal control problems in variable domains. Principle of the fictitious homogenization. Asymptot. Anal. 26 (2001) 37–72. [Google Scholar]
- P. Kogut and G. Leugering, On S-homogenization of an optimal control problem with control and state constraints. Z. Anal. Anwen. 20 (2001) 395–429. [CrossRef] [Google Scholar]
- P. Kogut and G. Leugering, Asymptotic analysis of state constrained semilinear optimal control problems. J. Optim. Theory Appl. 135 (2007) 301–321. [CrossRef] [MathSciNet] [Google Scholar]
- P. Kogut and G. Leugering, Homogenization of Dirichlet optimal control problems with exact partial controllability constraints. Asymptot. Anal. 57 (2008) 229–249. [MathSciNet] [Google Scholar]
- P. Kogut and G. Leugering, Optimal control problems for partial differential equations on reticulated domains. Approximation and asymptotic analysis. Systems & Control: Foundations & Applications. Birkhäuser/Springer, New York (2011). [Google Scholar]
- A. Lamacz, Dispersive effective models for waves in heterogeneous media. Math. Models Methods Appl. Sci. 21 (2011) 1871–1899. [CrossRef] [MathSciNet] [Google Scholar]
- A. Lamacz and B. Schweizer, Effective acoustic properties of a meta-material consisting of small Helmholtz resonators. Discrete Contin. Dyn. Syst. Ser. S 10 (2017) 815–835. [MathSciNet] [Google Scholar]
- J.-L. Lions, Contrôle optimal de systèmes gouvernés par des équations auxdérivées partielles. Dunod, Paris; Gauthier-Villars, Paris (1968). [Google Scholar]
- E. Sanchez-Palencia, Non-Homogeneous Media and Vibration Theory. Vol. 120 of Springer Lecture Notes in Physics (1980). [Google Scholar]
- F. Santosa and W. Symes, A dispersive effective medium for wave propagation in periodic composites. SIAM J. Appl. Math. 51 (1991) 984–1005. [CrossRef] [MathSciNet] [Google Scholar]
- F. Tröltzsch, Optimal Control of Partial Differential Equations. Grad. Stud. Math. 112. AMS, Providence, RI (2010). [CrossRef] [Google Scholar]
- I. Yousept, Optimal control of quasilinear H(curl)-elliptic partial differential equations in magnetostatic field problems. SIAM J. Control and Optim. 51 (2013) 3624–3651. [CrossRef] [MathSciNet] [Google Scholar]
- I. Yousept, Optimal control of non-smooth hyperbolic evolution Maxwell equations in type-II superconductivity. SIAM J. Control and Optim. 55 (2017) 2305–2332. [CrossRef] [MathSciNet] [Google Scholar]
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