Identifiability of Piecewise Constant Conductivity in a Heat Conduction Process

Gutman, Semion; Ha, Junhong

doi:10.1137/060657364

Cited by 14 publications

(31 citation statements)

References 9 publications

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“…This inversion procedure is accomplished by the Marching Algorithm described and justified in [7]. The Marching Algorithm ( [7], Theorem 4.6) is applied there to the identifiability of piecewise constant conductivities in a heat conduction problem.…”

Section: Identification Map and Its Continuitymentioning

confidence: 99%

“…The resulting sequence of M numbers (denoted by G) provides the input to the Marching Algorithm (see [7]) which uniquely recovers the sought parameter a(x).…”

Section: Introductionmentioning

confidence: 99%

“…In [7] and [8] we studied the conductivity identifiability problems and obtained some fundamental results (the Marching Algorithm, the continuity of the eigenvalues and the eigenfunctions) critical for the string vibration problems studied in this paper.…”

Section: Introductionmentioning

confidence: 99%

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Identifiability for Composite String Vibration Problem

Gutman¹,

Ha²

2010

Journal of the Korean Mathematical Society

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Abstract. The paper considers the identifiability (i.e., the unique identification) of a composite string in the class of piecewise constant parameters. The 1-D string vibration is measured at finitely many observation points. The observations are processed to obtain the first eigenvalue and a constant multiple of the first eigenfunction at the observation points. It is shown that the identification by the Marching Algorithm is continuous with respect to the mean convergence in the admissible set. The result is based on the continuous dependence of eigenvalues, eigenfunctions, and the solutions on the parameters. A numerical algorithm for the identification in the presence of noise is proposed and implemented.

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Section: Identification Map and Its Continuitymentioning

confidence: 99%

“…The resulting sequence of M numbers (denoted by G) provides the input to the Marching Algorithm (see [7]) which uniquely recovers the sought parameter a(x).…”

Section: Introductionmentioning

confidence: 99%

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Identifiability for Composite String Vibration Problem

Gutman¹,

Ha²

2010

Journal of the Korean Mathematical Society

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“…For piecewise-constant thermal conductivity coefficients a(x) with finitely many discontinuity points, IP 1 was studied recently in [2]. An inverse problem for equation (3) with different extra data, namely U (ξ n , t) for t > 0, ξ n ∈ [0, 1], 1 ≤ n ≤ N , min 1≤n≤N |ξ n − ξ n+1 | ≥ σ > 0, where σ is a fixed number, N = 3ν, and ν is the number of discontinuity points of a, was studied in [1].…”

mentioning

confidence: 99%

“…These standing assumptions about q j are not repeated in the formulation of the theorems below. Denote by M 0 the set of L 1 (0, 1) functions which change sign at most finitely many times in the interval [0,1].…”

mentioning

confidence: 99%

Property C for ODE and Applications to an Inverse Problem for a Heat Equation

Ramm

2009

Bull. Polish Acad. Sci. Math.

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Output feedback finite‐time boundary control for an unstable heat PDE with spatially varying coefficients

Ghaderi,

Mojallali

2024

Intl J Robust & Nonlinear

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This article studies the output feedback finite‐time boundary control for unstable heat systems with the spatially varying coefficient. First, a finite‐time observer with switched gains under a state‐dependent switching law is designed in order to estimate the states of the system in a finite‐time only exerting one displacement boundary measurement. Next, an observer‐based linear finite‐time control is planned. Namely, a linear switched control under a state‐dependent switching law is proposed to vanish every solution of an unstable heat partial differential equation with spatially varying coefficients in a finite time. We also present explicit forms for the proposed observer gains and output feedback finite‐time controller. Finally, some numerical simulations are provided to confirm the theoretical results.

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Identifiability of Piecewise Constant Conductivity in a Heat Conduction Process

Cited by 14 publications

References 9 publications

Identifiability for Composite String Vibration Problem

Identifiability for Composite String Vibration Problem

Property C for ODE and Applications to an Inverse Problem for a Heat Equation

Output feedback finite‐time boundary control for an unstable heat PDE with spatially varying coefficients

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