Reconstruction of Boundary Sources through Sensor Observations

Introduction. Problem Formulation. The paper deals with a problem of reconstruction of extremal boundary disturbances in a parabolic system. The reconstruction is perfomed on the basis of inaccurate observations of linear signals on system's states. Extremality of disturbances is understood with respect to a given linear functional. The paper ajoins theory of inverse problems for distributed systems (see, e.g., [Lavrentyev et al.,1980; Banks and Kunisch, 1982; Kurzhanski and Khapalov, 1989; Barbu, 1991; Osipov et al., 1991; Maksimov, 1993; Ainseba, 1994]) and theory of ill-posed problems (see, e.g., [Tikhonov and Arsenin, 1979], [Vasiliev, 1981]). A variant of a substantial problem formulation is as follows. A flow of heat enters a solid body occupying space\Omega through boundary domains fl 1 ; : : : ; fl n . At time t the instant velocity of the heat flow coming through fl k is represented as<F3