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 Num. Meth. Prog., 2016, Volume 17, Issue 3, Pages 280–290 (Mi vmp835)

Some control and inverse problems for linear parabolic equations

N. L. Gol'dman

Lomonosov Moscow State University, Research Computing Center

Abstract: Properties of solutions of control and inverse problems for one-dimensional parabolic equations with coefficients dependent on $(x,t)$ are studied. The proposed approach based on the duality principle allows one to generalize the known Lions' result on the density properties of averaged observations in control problems with a control function given in the initial conditions. It is shown that the significance of these density properties is not restricted to the control problems. Such properties are used to study inverse parabolic problems, in particular, to study the uniqueness conditions of their solutions.

Keywords: parabolic equations, control problems, duality principle, density property, controllability, inverse problems, adjoint problems, final overdetermination, uniqueness.

Full text: PDF file (247 kB)
UDC: 517.958

Citation: N. L. Gol'dman, “Some control and inverse problems for linear parabolic equations”, Num. Meth. Prog., 17:3 (2016), 280–290

Citation in format AMSBIB
\Bibitem{Gol16} \by N.~L.~Gol'dman \paper Some control and inverse problems for linear parabolic equations \jour Num. Meth. Prog. \yr 2016 \vol 17 \issue 3 \pages 280--290 \mathnet{http://mi.mathnet.ru/vmp835}