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Reconstruction of a convolution kernel in an integrodifferential problem with a fractional time derivative

Dedicated to Professor Jerome A. Goldstein in occasion of his eightieth birthday
The author is a member of GNAMPA of Istituto Nazionale di Alta Matematica.

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  • We consider the problem of reconstruction of a convolution kernel (together with the solution) for a linear abstract evolution equation with a fractional time derivative.

    Mathematics Subject Classification: Primary: 353030, 34K37, 26A33; Secondary: 37L05.


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  • [1] W. Arendt, C. J. K. Batty, M. Hieber and F. Neubrander, Vector-valued Laplace Transforms and Cauchy Problems, Monographs in Mathematics, vol. 96, Birkhäuser Verlag, 2001. doi: 10.1007/978-3-0348-5075-9.
    [2] J. Cheng, J. Nakagawa, M. Yamamoto and T. Yamazaki, Uniqueness in an inverse problem for a one-dimensional fractional diffusion equations, Inverse Problems, 25 (2009), 115002, 16 pp. doi: 10.1088/0266-5611/25/11/115002.
    [3] P. ClémentG. Gripenberg and S.-O. Londen, Schauder estimates for equations with fractional derivatives, Trans. Am. Math. Soc., 352 (2000), 2239-2260.  doi: 10.1090/S0002-9947-00-02507-1.
    [4] P. Clément, G. Gripenberg and S.-O. Londen, Regularity properties of solutions of fractional evolution equations, Lecture Notes in Pure and Applied Mathematics, 215 (2001), 235–246, Dekker, New York.
    [5] P. ClémentS.-O. Londen and G. Simonett, Quasilinear evolution equations and continuous interpolation spaces, J. Diff. Eq., 196 (2004), 418-447.  doi: 10.1016/j.jde.2003.07.014.
    [6] F. Colombo and D. Guidetti, A global in time existence and uniqueness result for a semilinear integrodifferential parabolic inverse problem in Sobolev spaces, Math. Models Methods Appl. Sci., 17 (2007), 1-29. 
    [7] F. Colombo and D. Guidetti, Some results in the identification of memory kernels, Operator Theory: Advances and Applications, 216 (2011), 121-138.  doi: 10.1007/978-3-0348-0069-3_7.
    [8] G. Da Prato and P. Grisvard, Sommes d'opérateurs linéaires et équations differentielles opérationelles, J. Math. Pures Appliquees, 54 (1975), 305-387. 
    [9] M. Di CristoD. Guidetti and A. Lorenzi, Abstract parabolic equations with applications to problems in cylindrical space domains, Ad. Diff. Eq., 15 (2010), 1-42. 
    [10] P. Feng and E. T. Karimov, Inverse source problems for time fractional mixed parabolic-hyperbolic-type equations, J. Inverse Ill-Posed Problems, 23 (2015), 339-353.  doi: 10.1515/jiip-2014-0022.
    [11] P. Grisvard, Commutativité de deux foncteurs d'interpolation et applications, J. Math. Pures Appl., 45 (1966), 143-206. 
    [12] D. Guidetti, On interpolation with boundary conditions, Math. Z., 207 (1991), 439-460.  doi: 10.1007/BF02571401.
    [13] D. Guidetti, Optimal regularity for mixed parabolic problems in spaces of functions which are Hölder continuous with respect to space variables, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 26 (1998), 763-790. 
    [14] D. Guidetti, On linear elliptic and parabolic problems in Nikol'skij spaces, Progress in nonlinear Differential Equations and their Applications, 80 (2011), 275-300.  doi: 10.1007/978-3-0348-0075-4_15.
    [15] D. Guidetti, On maximal regularity for abstract parabolic problems with fractional time derivative, Mediterr. J. Math., 16 (2019), Paper No. 40, 26 pp. doi: 10.1007/s00009-019-1309-y.
    [16] J. Janno, Determination of the order of fractional derivative and a kernel in an inverse problem for a generalized time fractional diffusion equation, Electronic Journal of Differential Equations, (2016), Paper No. 199, 28 pp.
    [17] J. Janno, Determination of time-dependent sources and parameters of nonlocal diffusion and wave equations from final data, Frac. Calc. Appl. Anal., 23 (2020), 1678-1701.  doi: 10.1515/fca-2020-0083.
    [18] J. Janno and K. Kasemets, Identification of a kernel in an evolutionary integral equation occurring in subdiffusion, J. Inverse Ill-Posed Problems, 25 (2017), 777-798.  doi: 10.1515/jiip-2016-0082.
    [19] N. Kinash and J. Janno, Inverse problems for a generalized subdiffusion equation with final overdetermination, Math. Model. Anal., 24 (2019), 236-262. 
    [20] A. Lorenzi and E. Sinestrari, An inverse problem in the theory of materials with memory, Nonlinear Anal., 12 (1988), 1317-1335.  doi: 10.1016/0362-546X(88)90080-6.
    [21] A. Lunardi, Interpolation Theory, Scuola Normale Superiore, 2009.
    [22] R. Metzler and J. Klafter, Boundary value problems for fractional diffusion equations, Physica A, 278 (2000), 107-125.  doi: 10.1016/S0378-4371(99)00503-8.
    [23] H. Tanabe, Equations of Evolution, Pitman, 1979.
    [24] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North Holland Mathematical Library, 18. North-Holland Publishing Co., Amsterdam-New York, 1978.
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