Inverse initial problem under Nash strategy for stochastic reaction-diffusion equations with dynamic boundary conditions

References

[1] E. M. Ait Ben Hassi, S.-E. Chorfi and L. Maniar, An inverse problem of radiative potentials and initial temperatures in parabolic equations with dynamic boundary conditions, J. Inverse Ill-Posed Probl. 30 (2022), no. 3, 363–378. 10.1515/jiip-2020-0067Suche in Google Scholar

[2] E. M. Ait Ben Hassi, S.-E. Chorfi and L. Maniar, Stable determination of coefficients in semilinear parabolic system with dynamic boundary conditions, Inverse Problems 38 (2022), no. 11, Article ID 115007. 10.1088/1361-6420/ac91edSuche in Google Scholar

[3] E. M. Ait Ben Hassi, S.-E. Chorfi, L. Maniar and O. Oukdach, Lipschitz stability for an inverse source problem in anisotropic parabolic equations with dynamic boundary conditions, Evol. Equ. Control Theory 10 (2021), no. 4, 837–859. 10.3934/eect.2020094Suche in Google Scholar

[4] M. Baroun, S. Boulite, A. Elgrou and L. Maniar, Null controllability for stochastic parabolic equations with dynamic boundary conditions, J. Dyn. Control Syst. 29 (2023), no. 4, 1727–1756. 10.1007/s10883-023-09656-ySuche in Google Scholar

[5] M. Baroun, S. Boulite, A. Elgrou and L. Maniar, Null controllability for backward stochastic parabolic convection-diffusion equations with dynamic boundary conditions, Math. Control Relat. Fields 15 (2025), no. 2, 615–639. 10.3934/mcrf.2024031Suche in Google Scholar

[6] M. Bellassoued and M. Yamamoto, Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems, Springer Monogr. Math., Springer, Tokyo, 2017. 10.1007/978-4-431-56600-7Suche in Google Scholar

[7] I. Boutaayamou, S.-E. Chorfi, L. Maniar and O. Oukdach, The cost of approximate controllability of heat equation with general dynamical boundary conditions, Port. Math. 78 (2021), no. 1, 65–99. 10.4171/pm/2061Suche in Google Scholar

[8] I. Boutaayamou, L. Maniar and O. Oukdach, Stackelberg–Nash null controllability of heat equation with general dynamic boundary conditions, Evol. Equ. Control Theory 11 (2022), no. 4, 1285–1307. 10.3934/eect.2021044Suche in Google Scholar

[9] I. Boutaayamou, L. Maniar and O. Oukdach, Time and norm optimal controls for the heat equation with dynamical boundary conditions, Math. Methods Appl. Sci. 45 (2022), no. 3, 1359–1376. 10.1002/mma.7857Suche in Google Scholar

[10] P. Brune, Dynamics of stochastic partial differential equations with dynamical boundary conditions, Dissertation, Universität Paderborn, Paderborn, 2012. Suche in Google Scholar

[11] P. Cannarsa and M. Yamamoto, Stability for backward problems in time for degenerate parabolic equations, preprint (2023), https://arxiv.org/abs/2305.00525. Suche in Google Scholar

[12] I. Chueshov and B. Schmalfuss, Parabolic stochastic partial differential equations with dynamical boundary conditions, Differential Integral Equations 17 (2004), no. 7–8, 751–780. 10.57262/die/1356060328Suche in Google Scholar

[13] G. M. Coclite, A. Favini, C. G. Gal, G. R. Goldstein, J. A. Goldstein, E. Obrecht and S. Romanelli, The role of Wentzell boundary conditions in linear and nonlinear analysis, Advances in Nonlinear Analysis: Theory Methods and Applications, Math. Probl. Eng. Aerosp. Sci. 3, Cambridge Science, Cambridge (2009), 277–289. Suche in Google Scholar

[14] F. Dou and W. Du, Determination of the solution of a stochastic parabolic equation by the terminal value, Inverse Problems 38 (2022), no. 7, Article ID 075010. 10.1088/1361-6420/ac72bcSuche in Google Scholar

[15] C. G. Gal, The role of surface diffusion in dynamic boundary conditions: Where do we stand?, Milan J. Math. 83 (2015), no. 2, 237–278. 10.1007/s00032-015-0242-1Suche in Google Scholar

[16] G. R. Goldstein, Derivation and physical interpretation of general boundary conditions, Adv. Differential Equations 11 (2006), no. 4, 457–480. 10.57262/ade/1355867704Suche in Google Scholar

[17] M. V. Klibanov, Inverse problems and Carleman estimates, Inverse Problems 8 (1992), no. 4, 575–596. 10.1088/0266-5611/8/4/009Suche in Google Scholar

[18] M. V. Klibanov and J. Li, Inverse Problems and Carleman Estimates—Global Uniqueness, Global Convergence and Experimental Data, Inverse Ill-posed Probl. Ser. 63, De Gruyter, Berlin, 2021. 10.1515/9783110745481Suche in Google Scholar

[19] Q. Lü, Carleman estimate for stochastic parabolic equations and inverse stochastic parabolic problems, Inverse Problems 28 (2012), no. 4, Article ID 045008. 10.1088/0266-5611/28/4/045008Suche in Google Scholar

[20] Q. Lü and X. Zhang, Inverse problems for stochastic partial differential equations: Some progresses and open problems, Numer. Algebra Control Optim. 14 (2024), no. 2, 227–272. 10.3934/naco.2023014Suche in Google Scholar

[21] L. Maniar, M. Meyries and R. Schnaubelt, Null controllability for parabolic equations with dynamic boundary conditions, Evol. Equ. Control Theory 6 (2017), no. 3, 381–407. 10.3934/eect.2017020Suche in Google Scholar

[22] O. Oukdach, S. Boulite, A. Elgrou and L. Maniar, Stackelberg–Nash null controllability for stochastic parabolic equations, preprint (2024), https://arxiv.org/abs/2407.20366. 10.1002/mma.11092Suche in Google Scholar

[23] O. Oukdach, S. Boulite, A. Elgrou and L. Maniar, Multi-objective control for stochastic parabolic equations with dynamic boundary conditions, J. Optim. Theory Appl. 204 (2025), no. 3, Paper No. 55. 10.1007/s10957-025-02623-6Suche in Google Scholar

[24] J. van Neerven, M. Veraar and L. Weis, Maximal L p -regularity for stochastic evolution equations, SIAM J. Math. Anal. 44 (2012), no. 3, 1372–1414. 10.1137/110832525Suche in Google Scholar

[25] M. Yamamoto, Carleman estimates for parabolic equations and applications, Inverse Problems 25 (2009), no. 12, Article ID 123013. 10.1088/0266-5611/25/12/123013Suche in Google Scholar

[26] Y. Yu and J.-F. Zhang, Two multiobjective problems for stochastic degenerate parabolic equations, SIAM J. Control Optim. 61 (2023), no. 4, 2708–2735. 10.1137/22M1510194Suche in Google Scholar