Geodesic
Some control and inverse problems for linear parabolic equations
Numerical methods and programming, Tome 17 (2016) no. 3, pp. 280-290.

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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.
Mots-clés : parabolic equations
Keywords: control problems, duality principle, density property, controllability, inverse problems, adjoint problems, final overdetermination, uniqueness. 
@article{VMP_2016_17_3_a8,
     author = {N. L. Gol'dman},
     title = {Some control and inverse problems for linear parabolic equations},
     journal = {Numerical methods and programming},
     pages = {280--290},
     publisher = {mathdoc},
     volume = {17},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2016_17_3_a8/}
}
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N. L. Gol'dman. Some control and inverse problems for linear parabolic equations. Numerical methods and programming, Tome 17 (2016) no. 3, pp. 280-290. http://geodesic.mathdoc.fr/item/VMP_2016_17_3_a8/