Identification of the Time Derivative Coefficient in a Fast Diffusion Degenerate Equation

A. Favini () and G. Marinoschi ()
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A. Favini: University of Bologna
G. Marinoschi: Institute of Mathematical Statistics and Applied Mathematics

Journal of Optimization Theory and Applications, 2010, vol. 145, issue 2, No 3, 249-269

Abstract: Abstract In this paper, we deal with the identification of the space variable time derivative coefficient u in a degenerate fast diffusion differential inclusion. The function u is vanishing on a subset strictly included in the space domain Ω. This problem is approached as a control problem (P) with the control u. An approximating control problem (P ε ) is introduced and the existence of an optimal pair is proved. Under certain assumptions on the initial data, the control is found in W 2,m (Ω), with m>N, in an implicit variational form. Next, it is shown that a sequence of optimal pairs $(u_{\varepsilon }^{\ast },y_{\varepsilon }^{\ast })$ of (P ε ) converges as ε goes to 0 to a pair (u *,y *) which realizes the minimum in (P), and y * is the solution to the original state system. An alternative approach to the control problem is done by considering two controls related between them by a certain elliptic problem. This approach leads to the determination of simpler conditions of optimality, but under an additional restriction upon the initial data of the direct problem.

Keywords: Identification problems; Fast diffusion differential inclusions; Degenerate parabolic PDEs; Flows in porous media (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-009-9635-z

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