Inverse Problems for Parabolic Differential Equations from Control Theory

Mohammed Al Horani, Angelo Favini

Abstract


We are concerned with some inverse problems related to parabolic first-order and second order linear differential equations in Hilbert spaces. All the results apply well to inverse problems for partial differential equations from mathematical physics and optimal control theory. Various concrete examples are described.

Keywords


Inverse problem; Hilbert space; Linear differential problem; First-Order differential equations; Second-Order differential equations

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References


M. Al Horani and A. Favini. Perturbation Method for First and Complete Second Order Differential Equations. J. Optim. Theory Appl., 130 (2015), 949-967.

M. Al Horani and A. Favini. Parabolic First and Second Order Differential Equations. To appear

M. Al Horani and A. Favini. An Identification Problem for First-Order Degenerate Differential Equations. J. Optim. Theory Appl., 130 (2006), 41-60.

M. Al Horani and A. Favini. Degenerate First-Order Inverse Problems In Banach Spaces. Nonlinear Analysis, Theory, Methods, and Applications, 75 (2012), 68-77.

M. Al Horani and A. Favini. Degenerate First-Order Identification Problems in Banach Spaces. In: Favini, A., Lorenzi, A.(eds.): Differential Equations Inverse and Direct Problems, Taylor and Francis Group, Boca Raton (2006), 1-15.

A. Favini, A. Lorenzi and H. Tanabe. Direct and Inverse Degenerate Parabolic Differential Equations with Multivalued Operators. Electron. J. Diff. Equ., 2015 (2015), 1-22.

A. Favini and H. Tanabe. Degenerate Differential Equations and Inverse Problems. In: A. Yagi, Y. Yamamoto (eds.): Partial Differential Equations, (2013), 89-100.

A. Favini and A. Yagi. Degenerate differential equations in Banach spaces, Marcel Dekker. Inc. New York, (1999).

I. Lasiecka and R. Triggiani. Control theory for partial differential equations. II. Abstract hyperbolic-like systems over a finite time horizon, Cambridge University Press, Cambridge, (2000).

J. L. Lions and E. Magenes. Non-homogeneous boundary value problems and applications, Springer-Verlag, Berlin, vol. 1 (1972).

A. Lunardi. Analytic semigroups and optimal regularity in parabolic problems, 1ist ed, Birkhäuser, Basel, (1995).

I. Prilepko, G. Orlovsky and A. Vasin. Methods for solving inverse problems in mathematical physics. Marcel Dekker. Inc. New York, (2000).

H. Triebel. Interpolation theory, function spaces, differential operators, North-Holland, Amesterdam, (1978).




DOI: 10.6092/issn.2240-2829/5887

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Copyright (c) 2015 Mohammed Al Horani, Angelo Favini

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