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- Title
RECOVERING A LARGE NUMBER OF DIFFUSION CONSTANTS IN A PARABOLIC EQUATION FROM ENERGY MEASUREMENTS.
- Authors
Mola, Gianluca
- Abstract
Let (H,<.,.>) be a separable Hilbert space and Ai : D(Ai)→H (i = 1,...,n) be a family of nonnegative and self-adjoint operators mutually commuting. We study the inverse problem consisting in the identification of a function u : [0; T] → H and n constants α1...αn0 (diffusion coeffcients) that fulll the initial-value problem ui(t) + α1A1u(t) + ...+αnAnu(t)ϵ(0,T); u(0)= x, and the additional conditions <A1u(T), u(T)>=φ1...,<Anu(T),u(T)i =φn; whereφiare given positive constants. Under suitable assumptions on the operators Ai and on the initial data x ϵ H, we shall prove that the solution of such a problem is unique and depends continuously on the data. We apply the abstract result to the identification of diffusion constants in a heat equation and of the Lamé parameters in a elasticity problem on a plate.
- Subjects
HILBERT space; ADJOINT operators (Quantum mechanics); INVERSE problems; ENERGY measurement; HEAT equation; INITIAL value problems
- Publication
Inverse Problems & Imaging, 2018, Vol 12, Issue 3, p527
- ISSN
1930-8337
- Publication type
Article
- DOI
10.3934/ipi.2018023