×

Inverse source problem for Sobolev equation with fractional Laplacian. (English) Zbl 1495.35216


MSC:

35R30 Inverse problems for PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
35K70 Ultraparabolic equations, pseudoparabolic equations, etc.
35R11 Fractional partial differential equations

References:

[1] Jin, L.; Li, L.; Fang, S., The global existence and time-decay for the solutions of the fractional pseudo-parabolic equation, Computers and Mathematics with Applications, 73, 10, 2221-2232 (2017) · Zbl 1386.35443 · doi:10.1016/j.camwa.2017.03.005
[2] Barenblatt, G. I.; Zheltov, I. P.; Kochina, I., Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks [strata], Journal of Applied Mathematics and Mechanics, 24, 5, 1286-1303 (1960) · Zbl 0104.21702 · doi:10.1016/0021-8928(60)90107-6
[3] Benjamin, T. B.; Bona, J. L.; Mahony, J. J., “Model equations for long waves in nonlinear dispersive systems”, Philosophical transactions of the Royal Society of London, Series A, Mathematical and Physical Sciences, 272, 1220, 47-78 (1972) · Zbl 0229.35013
[4] Wang, R.; Li, Y.; Wang, B., Random dynamics of fractional nonclassical diffusion equations driven by colored noise, Discrete & Continuous Dynamical Systems, 39, 7, 4091-4126 (2019) · Zbl 1414.37032 · doi:10.3934/dcds.2019165
[5] Wang, R.; Shi, L.; Wang, B., Asymptotic behavior of fractional nonclassical diffusion equations driven by nonlinear colored noise on \(R^N\), Nonlinearity, 32, 11, 4524-4556 (2019) · Zbl 1423.35419
[6] Wang, R.; Li, Y.; Wang, B., Bi-spatial pullback attractors of fractional nonclassical diffusion equations on unbounded domains with (p, q)-growth nonlinearities, Applied Mathematics and Optimization, 84, 1, 425-461 (2021) · Zbl 1476.37091 · doi:10.1007/s00245-019-09650-6
[7] Tuan, N. H.; Caraballo, T., On initial and terminal value problems for fractional nonclassical diffusion equations, Proceedings of the American Mathematical Society, 149, 1, 143-161 (2021) · Zbl 1456.35222 · doi:10.1090/proc/15131
[8] Tuan, N. H.; Au, V. V.; Xu, R., Semilinear Caputo time-fractional pseudo-parabolic equations, Communications on Pure & Applied Analysis, 20, 2, 583-621 (2021) · Zbl 1460.35381 · doi:10.3934/cpaa.2020282
[9] Warma, M.; Antil, H.; Verma, D., Optimal control of fractional elliptic PDEs with state constraints and characterization of the dual of fractional-order Sobolev spaces, Journal of Optimization Theory and Applications, 186, 1, 1-23 (2020) · Zbl 1443.49005 · doi:10.1007/s10957-020-01684-z
[10] Antil, H.; Warma, M., Optimal control of fractional semilinear PDEs, ESAIM, 26, 130 (2020) · Zbl 1439.49008
[11] Antil, H.; Verma, D.; Warma, M., External optimal control of fractional parabolic PDEs, ESAIM, 26, 20 (2020) · Zbl 1444.35144 · doi:10.1051/cocv/2020005
[12] Warma, M.; Antil, H.; Khatri, R., External optimal control of nonlocal PDEs, Inverse Problems, 35, 8, 084003 (2019) · Zbl 1461.35221 · doi:10.1088/1361-6420/ab1299
[13] Warma, M.; Antil, H., Optimal control of the coefficient for fractional and regional fractional \(p\)-Laplace equations: approximation and convergence, Mathematical Control and Related Fields, 9, 1-38 (2019) · Zbl 1423.35388
[14] Luc, N. H.; Long, L. D.; Hang, L. T. D.; Baleanu, D.; Can, N. H., Identifying the initial condition for space-fractional Sobolev equation, Journal of Applied Analysis & Computation, 11, 5, 2402-2422 (2021) · Zbl 07907283 · doi:10.11948/20200404
[15] Au, V. V.; Hossein, J.; Hammouch, Z.; Tuan, N. H., On a final value problem for a nonlinear fractional pseudo-parabolic equation, Electronic Research Archive, 29, 1, 1709-1734 (2021) · Zbl 1456.35114 · doi:10.3934/era.2020088
[16] Nam, D. H. Q.; O’Regan, D.; Long, L. D.; Ngoc, T. B.; Tuan, N. H., Identification of the righthand side in a bi-parabolic equation with final data, Applicable Analysis, 101 (2020)
[17] Ma, Y. K.; Prakash, P.; Deiveegan, A., Generalized Tikhonov methods for an inverse source problem of the time- fractional diffusion equation, Chaos, Solitons and Fractals, 108, 39-48 (2018) · Zbl 1390.35425 · doi:10.1016/j.chaos.2018.01.003
[18] Engl, H. W.; Hanke, M.; Neubauer, A., Regularization of Inverse Problems (1996), Boston: Kluwer Academic, Boston · Zbl 0859.65054 · doi:10.1007/978-94-009-1740-8
[19] Han, Y.; Xiong, X.; Xue, X., A fractional Landweber method for solving backward time-fractional diffusion problem, Computers & Mathematcs with Applications, 78, 1, 81-91 (2019) · Zbl 1442.65224 · doi:10.1016/j.camwa.2019.02.017
[20] Jiang, Z. S.; Wu, J. Y., Recovering space-dependent source for a time-space fractional diffusion wave equation by fractional Landweber method, Inverse Problems in Science and Engineering, 29, 7, 990-1011 (2021) · Zbl 1473.65167 · doi:10.1080/17415977.2020.1815724
[21] Yang, F.; Fu, L. J.; Fan, P.; Li, X. X., Fractional Landweber iterative regularization method for identifying the unknown source of the time-fractional diffusion problem, Acta Applicandae Mathematicae, 175, 1 (2021) · Zbl 1476.35339 · doi:10.1007/s10440-021-00442-1
[22] Binh, T. T.; Nashine, H. K.; Le, D. L.; Nguyen, H. L.; Can, N., Identification of source term for the ill-posed Rayleigh-Stokes problem by Tikhonov regularization method, Advances in Difference Equations, 2019, 1 (2019) · Zbl 1485.35416 · doi:10.1186/s13662-019-2261-7
[23] Tuan, N. H.; Long, L. D.; Thinh, N. V., Regularized solution of an inverse source problem for a time fractional diffusion equation, Applied Mathematical Modelling, 40, 19-20, 8244-8264 (2016) · Zbl 1471.65124 · doi:10.1016/j.apm.2016.04.009
[24] Bakushinsky, A. B.; Kokurin, M. Y.; Smirnova, A., Iterative Methods for Ill-Posed Problems (2011), Inverse and Ill-Posed Problems Series · Zbl 1215.47013
[25] Louis, A. K., Inverse und Schlecht Gestellte Probleme (2013), Springer-Verlag
[26] Can, N. H.; Luc, N. H.; Baleanu, D.; Zhou, Y., Inverse source problem for time fractional diffusion equation with Mittag-Leffler kernel, Advances in Difference Equations, 1 (2020) · Zbl 1482.35272
[27] Tuan, N. H.; O’regan, D.; Ngoc, T. B., Continuity with respect to fractional order of the time fractional diffusion-wave equation, Evolution Equations & Control Theory, 9, 3, 773-793 (2020) · Zbl 1455.35295 · doi:10.3934/eect.2020033
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.