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Uniqueness and nonuniqueness in an inverse problem for the parabolic equation. (English) Zbl 0519.35077

MSC:
35R30 Inverse problems for PDEs
35K05 Heat equation
93B30 System identification
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[1] Coddington, E.A; Levinson, N, Theory of ordinary differential equations, (1955), McGraw-Hill New York/Toronto/London · Zbl 0042.32602
[2] Gel’fand, I.M; Levitan, B.M; Gel’fand, I.M; Levitan, B.M, On the determination of a differential equation from its spectral function, Izv. acad. nauk SSSR ser. mat., Amer. math. soc. transl. ser. 2, 1, No. 4, 253-304, (1955), [English transl.] · Zbl 0066.33603
[3] Kitamura, S; Nakagiri, S, Identification of spatially-varying and constant parameters in distributed systems of parabolic type, SIAM J. control optim., 15, 785-802, (1977) · Zbl 0354.93020
[4] Levitan, B.M; Sargsjan, I.S, Introduction to spectral theory, () · Zbl 0302.47036
[5] \scR. Murayama, The Gel’fand-Levitan theory and certain inverse problems for the parabolic equation, J. Fac. Sci. Univ. Tokyo, in press. · Zbl 0485.35082
[6] Pierce, A, Unique identification of eigenvalues and coefficients in a parabolic problem, SIAM J. control optim., 17, 494-499, (1979) · Zbl 0415.35035
[7] Suzuki, T; Murayama, R, A uniqueness theorem in an identification problem for coefficients of parabolic equations, (), 259-263 · Zbl 0473.35076
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