On the solvability of an inverse problem for the Burgers equation with an integral overdetermination condition in a nonlinearly degenerating domain

References

[1] R. A. Adams and J. J. F. Fournier, Sobolev Spaces, 2nd ed., Pure Appl. Math. (Amsterdam) 140, Elsevier/Academic, Amsterdam, 2003. Search in Google Scholar

[2] J. Apraiz, A. Doubova, E. Fernández-Cara and M. Yamamoto, Some inverse problems for the Burgers equation and related systems, Commun. Nonlinear Sci. Numer. Simul. 107 (2022), Article ID 106113. 10.1016/j.cnsns.2021.106113Search in Google Scholar

[3] I. Bağlan, A. O. Akdemir and M. A. Dokuyucu, Inverse coefficient problem for quasilinear pseudo-parabolic equation by Fourier method, Filomat 37 (2023), no. 21, 7217–7230. 10.2298/FIL2321217BSearch in Google Scholar

[4] I. Baglan and F. Kanca, Two-dimensional inverse quasilinear parabolic problem with periodic boundary condition, Appl. Anal. 98 (2019), no. 8, 1549–1565. 10.1080/00036811.2018.1434149Search in Google Scholar

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

[6] X. Cheng, Z. Fu and B. Wetton, Equivalent formulations of the oxygen depletion problem, other implicit moving boundary value problems, and implications for numerical approximation, SIAM J. Appl. Math. 83 (2023), no. 1, 52–78. 10.1137/21M1419167Search in Google Scholar

[7] S. De Lillo, Moving boundary problems for the Burgers equation, Inverse Problems 14 (1998), no. 1, 1–4. 10.1088/0266-5611/14/1/001Search in Google Scholar

[8] A. Hasanov Hasanoğlu and V. G. Romanov, Introduction to Inverse Problems for Differential Equations, Springer, Cham, 2017. 10.1007/978-3-319-62797-7Search in Google Scholar

[9] M. S. Hussein, D. Lesnic, V. L. Kamynin and A. B. Kostin, Direct and inverse source problems for degenerate parabolic equations, J. Inverse Ill-Posed Probl. 28 (2020), no. 3, 425–448. 10.1515/jiip-2019-0046Search in Google Scholar

[10] N. Huzyk, Inverse problem of determining the coefficients in a degenerate parabolic equation, Electron. J. Differential Equations 2014 (2014), Paper No. 172. Search in Google Scholar

[11] N. Huzyk, Inverse free boundary problems for a generally degenerate parabolic equation, J. Inverse Ill-Posed Probl. 23 (2015), no. 2, 103–119. 10.1515/jiip-2011-0016Search in Google Scholar

[12] V. Isakov, Inverse Problems for Partial Differential Equations, Appl. Math. Sci. 127, Springer, New York, 2006. Search in Google Scholar

[13] M. Jenaliyev, M. Ramazanov and M. Yergaliyev, On the coefficient inverse problem of heat conduction in a degenerating domain, Appl. Anal. 99 (2020), no. 6, 1026–1041. 10.1080/00036811.2018.1518523Search in Google Scholar

[14] M. Jenaliyev, M. Ramazanov and M. Yergaliyev, On the numerical solution of one inverse problem for a linearized two-dimensional system of Navier-Stokes equations, Opuscula Math. 42 (2022), no. 5, 709–725. 10.7494/OpMath.2022.42.5.709Search in Google Scholar

[15] M. T. Jenaliyev, M. A. Bektemesov and M. G. Yergaliyev, On an inverse problem for a linearized system of Navier–Stokes equations with a final overdetermination condition, J. Inverse Ill-Posed Probl. 31 (2023), no. 4, 611–624. 10.1515/jiip-2022-0065Search in Google Scholar

[16] S. I. Kabanikhin, Inverse and Ill-Posed Problems, Inverse Ill-posed Probl. Ser. 55, Walter de Gruyter, Berlin, 2012. 10.1515/9783110224016Search in Google Scholar

[17] I. V. Kravchenko, V. V. Kravchenko and S. M. Torba, Solution of parabolic free boundary problems using transmuted heat polynomials, Math. Methods Appl. Sci. 42 (2019), no. 15, 5094–5105. 10.1002/mma.5483Search in Google Scholar

[18] J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications. Vol. 1, Dunod, Paris, 1968. Search in Google Scholar

[19] D. V. Lukyanenko, A. A. Borzunov and M. A. Shishlenin, Solving coefficient inverse problems for nonlinear singularly perturbed equations of the reaction-diffusion-advection type with data on the position of a reaction front, Commun. Nonlinear Sci. Numer. Simul. 99 (2021), Article ID 105824. 10.1016/j.cnsns.2021.105824Search in Google Scholar

[20] D. V. Lukyanenko, I. V. Prigorniy and M. A. Shishlenin, Some features of solving an inverse backward problem for a generalized Burgers’ equation, J. Inverse Ill-Posed Probl. 28 (2020), no. 5, 641–649. 10.1515/jiip-2020-0078Search in Google Scholar

[21] D. V. Lukyanenko, M. A. Shishlenin and V. T. Volkov, Solving of the coefficient inverse problems for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time data, Commun. Nonlinear Sci. Numer. Simul. 54 (2018), 233–247. 10.1016/j.cnsns.2017.06.002Search in Google Scholar

[22] S. L. Mitchell, N. P. McInerney and S. B. G. O’Brien, Approximate solution techniques for the sorption of a finite amount of swelling solvent in a glassy polymer, Appl. Math. Model. 92 (2021), 624–650. 10.1016/j.apm.2020.11.018Search in Google Scholar

[23] P. M. Nguyen and L. H. Nguyen, A numerical method for an inverse source problem for parabolic equations and its application to a coefficient inverse problem, J. Inverse Ill-Posed Probl. 28 (2020), no. 3, 323–339. 10.1515/jiip-2019-0026Search in Google Scholar

[24] Y. H. Ou, A. Hasanov and Z. H. Liu, Inverse coefficient problems for nonlinear parabolic differential equations, Acta Math. Sin. (Engl. Ser.) 24 (2008), no. 10, 1617–1624. 10.1007/s10114-008-6384-0Search in Google Scholar

[25] M. A. Rincon and A. Scardua, The Stefan problem with moving boundary, Bol. Soc. Parana. Mat. (3) 26 (2008), no. 1–2, 91–106. 10.5269/bspm.v26i1-2.7412Search in Google Scholar

[26] V. G. Romanov, Investigation Methods for Inverse Problems, Inverse Ill-posed Probl. Ser., VSP, Utrecht, 2002. 10.1515/9783110943849Search in Google Scholar

[27] M. Yergaliyev, M. Jenaliyev, A. Romankyzy and A. Zholdasbek, On an inverse problem with an integral overdetermination condition for the Burgers equation, J. Math. Mech. Comp. Sci. 117 (2023), 24–41. 10.26577/JMMCS.2023.v117.i1.03Search in Google Scholar