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Inverse problems on degenerate integro-differential equations

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  • We study inverse problems on degenerate integro-differential equations without using maximal regularity property. This seems new at all in the related literature. Some applications to concrete partial differential equations are given.

    Mathematics Subject Classification: Primary: 35R09; Secondary: 45J05.

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  • [1] M. Al Horani and A. Favini, Degenerate first-order identification problems in Banach spaces, Differential Equations, Inverse and Direct Problems, Taylor and Francis Group, Boca Raton (eds. A. Favini and A. Lorenzi), 1–15, Lect. Notes Pure Appl. Math., 251, Chapman & Hall/CRC, Boca Raton, FL, 2006.
    [2] M. Al Horani and A. Favini, An identification problem for first-order degenerate differential equations, J. Optim. Theory Appl., 130 (2006), 41-60.  doi: 10.1007/s10957-006-9083-y.
    [3] A. Favaron and A. Favini, On the behaviour of singular semigroups in intermediate and interpolation spaces and its applications to maximal regularity for degenerate integro-differential evolution equations, Abstr. Appl. Anal., 2013 (2013), Art. ID 275494, 37 pp. doi: 10.1155/2013/275494.
    [4] A. Favini and H. Tanabe, Perturbation methods for inverse problems on degenerate differential equations, J. Math. Soc. Japan, submitted.
    [5] A. Favini and A. Yagi, Degenerate Differential Equations in Banach Spaces, Marcel Dekker. Inc., New York, 1999.
    [6] P. Grisvard, Spazi di tracce e applicazioni, Rend. Mat., 5 (1972), 657-729. 
    [7] P. Grisvard, Commutativité de Deux Foncteurs d'interpolation et applications, J. Math. Pures Appl., 45 (1966), 207-290. 
    [8] J.-L. Lions and J. Peetre, Sur une classe d'espaces d'interpolation, Inst. Hautes Études Sci. Publ. Math., 19 (1964), 5-68. 
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