Voir la notice de l'article provenant de la source Library of Science
@article{IJAMCS_2020_30_1_a0,
author = {Maksimov, Vyacheslav and Trl\"otzsch, Fredi},
title = {Input reconstruction by feedback control for the {Schl\"ogl} and {FitzHugh{\textendash}Nagumo} equations},
journal = {International Journal of Applied Mathematics and Computer Science},
pages = {5--22},
publisher = {mathdoc},
volume = {30},
number = {1},
year = {2020},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IJAMCS_2020_30_1_a0/}
}
TY - JOUR AU - Maksimov, Vyacheslav AU - Trlötzsch, Fredi TI - Input reconstruction by feedback control for the Schlögl and FitzHugh–Nagumo equations JO - International Journal of Applied Mathematics and Computer Science PY - 2020 SP - 5 EP - 22 VL - 30 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/IJAMCS_2020_30_1_a0/ LA - en ID - IJAMCS_2020_30_1_a0 ER -
%0 Journal Article %A Maksimov, Vyacheslav %A Trlötzsch, Fredi %T Input reconstruction by feedback control for the Schlögl and FitzHugh–Nagumo equations %J International Journal of Applied Mathematics and Computer Science %D 2020 %P 5-22 %V 30 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/IJAMCS_2020_30_1_a0/ %G en %F IJAMCS_2020_30_1_a0
Maksimov, Vyacheslav; Trlötzsch, Fredi. Input reconstruction by feedback control for the Schlögl and FitzHugh–Nagumo equations. International Journal of Applied Mathematics and Computer Science, Tome 30 (2020) no. 1, pp. 5-22. http://geodesic.mathdoc.fr/item/IJAMCS_2020_30_1_a0/
[1] Avdonin, S. and Bell, J. (2015). Determining a distributed conductance parameter for a neuronal cable model defined on a tree graph, Journal of Inverse Problems and Imaging 9(3): 645–659.
[2] Banks, H.T. and Kunisch, K. (1989). Estimation Techniques for Distributed Parameter Systems, Birkhäuser, Boston, MA.
[3] Barbu, V. (1990). The inverse one phase Stefan problem, Differential Integral Equations 3(2): 209–218.
[4] Breiten, T. and Kunisch, K. (2014). Riccati-based feedback control of the monodomain equations with the FitzHugh–Nagumo model, SIAM Journal of Control and Optimization 52(6): 4057–4081.
[5] Buchholz, R., Engel, H., Kammann, E. and Tröltzsch, F. (2013). On the optimal control of the Schlögl-model, Computational Optimization and Application 56(1): 153–185.
[6] Casas, E., Ryll, C. and Tröltzsch, F. (2013). Sparse optimal control of the Schlögl and FitzHugh–Nagumo systems, Computational Methods in Applied Mathematics 13(4): 415–442.
[7] Evans, L.C. (1998). Partial Differential Equations, American Mathematical Society, Providence, RI. Gugat, M. and Tröltzsch, F. (2015). Boundary feedback stabilization of the Schlögl system, Automatica 51(C): 192–199.
[8] Jackson, D.E. (1990). Existence and regularity for the FitzHugh–Nagumo equations with inhomogeneous boundary conditions, Nonlinear Analysis: Theory, Methods Applications A: Theory and Methods 14(3): 201–216.
[9] Kabanikhin, S.I. (2011). Inverse and Ill-posed Problems, De Gruyter, Berlin.
[10] Krasovskii, N.N. and Subbotin, A.I. (1988). Game-Theoretical Control Problems, Springer Verlag, New York, NY/Berlin.
[11] Kryazhimskii, A.V., Osipov, Yu. S., (1995). Inverse Problems for Ordinary Differential Equations: Dynamical Solutions, Gordon and Breach, London.
[12] Lasiecka, I., Triggiani, R., and Yao, P.F. (1999). Inverse/observability estimates for second order hyperbolic equations with variable coefficients, Journal of Mathematical Analysis and Applications 235(1): 13–57.
[13] Lavrentiev, M.M., Romanov, V.G., and Shishatskii, S.P. (1980). Ill-posed Problems of Mathematical Physics and Analysis, Nauka, Novosibirsk, (in Russian).
[14] Le, M.H.L. (2019). Eine Methode der Steuerungs-Rekonstruktion bei semilinearen parabolischen Differentialgleichungen, Master thesis, Technische Universität Berlin, Berlin.
[15] Maksimov, V. (2002). Dynamical Inverse Problems of Distributed Systems, VSP, Utrecht/Boston, MA.
[16] Maksimov, V. (2009). On reconstruction of boundary controls in a parabolic equations, Advances in Differential Equations 14(11–12): 1193–1211.
[17] Maksimov, V. (2016). Game control problem for a phase field equation, Journal Optimization Theory and Applications 170(1): 294–307.
[18] Maksimov, V. (2017). Some problems of guaranteed control of the Schlögl and FitzHugh–Nagumo systems, Evolution Equations and Control Theory 6(4): 559–586.
[19] Maksimov, V. and Mordukhovich, B.S. (2017). Feedback design of differential equations of reconstruction for second-order distributed systems, International Journal of Applied Mathematics and Computer Science 27(3): 467–475, DOI: 10.1515/amcs-2017-0032.
[20] Maksimov, V. and Pandolfi, L. (2002). The problem of dynamical reconstruction of Dirichlet boundary control in semilinear hyperbolic equations, Journal of Inverse and Ill-Posed Problems 8(4): 399–411.
[21] Mordukhovich, B.S. (2008). Optimization and feedback design of state-constrained parabolic systems, Pacific Journal of Optimization 4(3): 549–570.
[22] Ryll, C., Löber, J., Martens, S., Engel, H., and Tröltzsch, F. (2016). Analytical, optimal, and sparse optimal control of traveling wave solutions to reaction-diffusion systems, in F. Schöll et al. (Eds.), Control and Self-Organizing Nonlinear Systems, Springer, Berlin, pp. 189–210.
[23] Samarskii, A.A. (1971). Introduction to the Theory of Difference Schemes, Nauka, Moscow, (in Russian).
[24] Shitao, L. and Triggiani, R. (2013). Recovering damping and potential coefficients for an inverse non-homogeneous second-order hyperbolic problem via a localized Neumann boundary trace, Discrete and Continuous Dynamical Systems 33(1112): 5217–5252.
[25] Tikhonov, A.N. and Arsenin, V.Y. (1977). Solutions of Ill-posed Problems, V.H. Winston Sons, Washington, DC.