Perturbative methods for inverse problems on degenerate differential equations

Angelo Favini

Abstract


Pertubation results for linear relations satisfying a resolvent condition of weak parabolic type are established. Such results are applied to solve some inverse problems for degenerate differential equations, supplying a new method which avoids any fixed-point argument and essentially consists in reducing the original inverse problem to an auxiliary direct one.

Keywords


pertubative methods; inverse problems; degenerate differential equations

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References


M. Al Horani, A. Favini, Degenerate first order identfiication problems in Banach spaces, Differential Equations; Inverse and Direct Problems, Edited by A. Favini and A. Lorenzi, Taylor and Francis

Group, New York, N.Y. 2006, 1-15.

M. Al Horani, A. Favini, An identication problem for first-order degenerate differential equations, Journal of Optimization Theory and Applications, Vol. 130, Number 1 (2006), 41-60.

R. Cross, Multivalued Linear Operators, M. Dekker, Inc., 1998.

R. Cross, A. Favini and Ya. Yakubov, Perturbation results for multivalued linear operators, Parabolic Problems: the Herbert Amann Festschrift, J. Escher, P. Guidotti, M. Hieber, P. M. Bucha, J. W. Pruss, Y. Shibata, G. Simonett, C. Walker, W Zajaczkowski Editors, Birkhauser Basel AG, 2011, 111-130.

A. Favaron, A. Favini, Fractional powers in interpolation theory for multivalued linear operators and applications to degenerate differential equations, Tsukuba J. of Mathematics Vol. 35, No.2 (2011), 259-323.

A. Favaron, 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, submitted.

A. Favaron, A. Favini, Perturbation methods for inverse problems on degenerate differential equations, submitted.

A. Favini, Perturbation methods and identication problems for degenerate evolution systems, VII Congress of Romanian Mathematicians, June 29 - July 5, 2011, Brasov, Romania.

A. Favini, A. Lorenzi, H. Tanabe and A. Yagi, An Lp-approach to singular linear parabolic equations in bounded domains, Osaka J. Math. 42 (2005), 385-406.

A. Favini, A. Yagi, Degenerate Dierential Equations in Banach Spaces, Marcel Dekker, Inc., New York, 1999.

A. Lunardi, Analytic semigroups amd optimal regularity in parabolic problems, Birkhauser, Basel, 1995.

W. von Wahl, Gebrochene Potenzen eines elliptischen Operators und parabolische Differentialgleichungen

in Raumen hoelderstetiger Funktionen, Nachr. Akad. Wiss. Gottingen Math.-Phys. Kl. II, (1972), 231258.




DOI: 10.6092/issn.2240-2829/3422

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