References
- Amstutz, S. (2005). The topological asymptotic for the Navier–Stokes equations, ESAIM: Control, Optimization and Calculus of Variations 11(3): 401–425.
- Amstutz, S. (2006). Topological sensitivity analysis for some nonlinear PDE systems, Journal de Mathématiques Pures et Appliquées 85(4): 540–557.
- Baumann, P. and Sturm, K. (2022). Adjoint-based methods to compute higher-order topological derivatives with an application to elasticity, Engineering Computations 39(1): 60–114.
- Bewley, T.R., Temam, R. and Ziane, M. (2000). A general framework for robust control in fluid mechanics, Physica D: Nonlinear Phenomena 138(3–4): 360–392.
- Bogachev, V.I. and Ruas, M.A.S. (2007). Measure Theory, Vol. 1, Springer, Berlin.
- Boyer, F. and Fabrie, P. (2005). Eléments d’analyse pour l’étude de quelques modèles d’écoulements de fluides visqueux incompressibles, Springer, Berlin.
- Brett, C.E. (2014). Optimal Control and Inverse Problems Involving Point and Line Functionals and Inequality Constraints, PhD thesis, University of Warwick, Coventry.
- Caubet, F. and Dambrine, M. (2012). Localization of small obstacles in Stokes flow, Inverse Problems 28(10): 105007.
- Dáger, R. (2006). Insensitizing controls for the 1-D wave equation, SIAM Journal on Control and Optimization 45(5): 1758–1768.
- Dziri, R., Moubachir, M. and Zolésio, J.-P. (2004). Dynamical shape gradient for the Navier–Stokes system, Comptes Rendus Mathematique 338(2): 183–186.
- Dziri, R. and Zolésio, J.-P. (2011). Drag reduction for non-cylindrical Navier–Stokes flows, Optimization Methods and Software 26(4–5): 575–600.
- Ekeland, I. and Temam, R. (1999). Convex Analysis and Variational Problems, SIAM, Philadelphia.
- Ervedoza, S., Lissy, P. and Privat, Y. (2022). Desensitizing control for the heat equation with respect to domain variations, Journal de l’École Polytechnique Mathématiques 9: 1397–1429.
- Galdi, G. (2011). An Introduction to the Mathematical Theory of the Navier–Stokes Equations: Steady-State Problems, Springer, New York.
- Garreau, S., Guillaume, P. and Masmoudi, M. (2001). The topological asymptotic for PDE systems: The elasticity case, SIAM Journal on Control and Optimization 39(6): 1756–1778.
- Giusti, S.M., Sokołowski, J. and Stebel, J. (2015). On topological derivatives for contact problems in elasticity, Journal of Optimization Theory and Applications 165: 279–294.
- Guerrero, S. (2007). Controllability of systems of Stokes equations with one control force: Existence of insensitizing controls, Annales de l’Institut Henri Poincaré C, Analyse non linéaire 24(6): 1029–1054.
- Gueye, M. (2013). Insensitizing controls for the Navier–Stokes equations, Annales de l’Institut Henri Poincaré C, Analyse non linéaire 30(5): 825–844.
- Gugat, M. and Lazar, M. (2023). Optimal control problems without terminal constraints: The turnpike property with interior decay, International Journal of Applied Mathematics and Computer Science 33(3): 429–438, DOI: 10.34768/amcs-2023-0031.
- Gugat, M. and Sokołowski, J. (2023). An aspect of the turnpike property: Long time horizon behavior, Serdica Mathematical Journal 49(1–3): 127–154.
- Guillaume, P. and Hassine, M. (2008). Removing holes in topological shape optimization, ESAIM: Control, Optimisation and Calculus of Variations 14(1): 160–191.
- Hassine, M. and Masmoudi, M. (2004). The topological asymptotic expansion for the quasi-Stokes problem, ESAIM: Control, Optimisation and Calculus of Variations 10(4): 478–504.
- Hlaváček, I., Novotny, A., Sokołowski, J. and ˙Zochowski, A. (2009). On topological derivatives for elastic solids with uncertain input data, Journal of Optimization Theory and Applications 141(3): 569–595.
- Iguernane, M., Nazarov, S.A., Roche, J.-R., Sokolowski, J. and Szulc, K. (2009). Topological derivatives for semilinear elliptic equations, International Journal of Applied Mathematics and Computer Science 19(2): 191–205, DOI: 10.2478/v10006-009-0016-4.
- Kovtunenko, V.A. and Kunisch, K. (2014). High precision identification of an object: Optimality-conditions-based concept of imaging, SIAM Journal on Control and Optimization 52(1): 773–796.
- Krzy˙zanowski, P., Malikova, S., Mucha, P. B. and Piasecki, T. (2024). Comparative analysis of obstacle approximation strategies for the steady incompressible Navier–Stokes equations, Applied Mathematics & Optimization 89(2): 1–20.
- Leugering, G., Novotny, A.A. and Sokołowski, J. (2022). On the robustness of the topological derivative for Helmholtz problems and applications, Control and Cybernetics 51(2): 227–248.
- Lions, J. (1992). Sentinelles pour les Systmès Distribuésà Données Incomplètes, Masson, Paris.
- Logg, A., Mardal, K.-A. and Wells, G. (2012). Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book, Springer, Berlin.
- Moubachir, M. and Zolesio, J.-P. (2006). Moving Shape Analysis and Control: Applications to Fluid Structure Interactions, Chapman and Hall/CRC, Boca Raton.
- Novotny, A.A. and Sokołowski, J. (2012). Topological Derivatives in Shape Optimization, Springer, Berlin.
- Novotny, A.A., Sokołowski, J. and ˙Zochowski, A. (2019). Applications of the Topological Derivative Method, Springer, Cham.
- Sá, N.L., Amigo, R.R., Novotny, A.A. and Silva, N.E. (2016). Topological derivatives applied to fluid flow channel design optimization problems, Structural and Multidisciplinary Optimization 54: 249–264.
- Sokołowski, J. and ˙Zochowski, A. (1999). On the topological derivative in shape optimization, SIAM Journal on Control and Optimization 37(4): 1251–1272.
- Sokołowski, J. and Zolésio, J.-P. (1992). Introduction to Shape Optimization, Springer, Berlin.
- Sturm, K. (2020). Topological sensitivities via a Lagrangian approach for semilinear problems, Nonlinearity 33(9): 4310.
- Szabó, B. and Babuška, I. (2011). Introduction to Finite Element Analysis: Formulation, Verification and Validation, Wiley, Chichester.
- Tröltzsch, F. (2024). Optimal Control of Partial Differential Equations: Theory, Methods and Applications, American Mathematical Society, Providence.