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Inverse problems for the heat equation with time dependent conductivity. (Italian. English summary) Zbl 0589.35052

Pubbl., Ser. III, Ist. Appl. Calcolo 219, 20 pp. (1983).
Summary: The determination of the unknown coefficient a(t), in the equation \(u_ t=a(t)u_{xx}\), from various situations of overspecified initial- boundary data is considered. These problems are not properly posed in the sense of Hadamard.
By imposing some ”a priori” constraints, functional classes of admissible coefficients in which the maps: ”data”\(\to ''coefficient''\) are Hölder- continuous is determined.

MSC:

35K05 Heat equation
35R30 Inverse problems for PDEs
35R25 Ill-posed problems for PDEs