Geodesic
Controllability of parabolic equations
Sbornik. Mathematics, Tome 186 (1995) no. 6, pp. 879-900

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This paper studies two problems of exact controllability of semilinear parabolic equations. In the first, the control is on the right-hand side of the parabolic equation and distributed over an arbitrary subdomain $\omega$ of the domain $\Omega$. In the second, the control is contained in the boundary conditions and distributed over a subdomain $\Gamma_0$ of the boundary $\partial\Omega$. If the original data satisfy certain conditions, then both problems are solvable. 
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     author = {Yu. S. \`Emanuilov},
     title = {Controllability of parabolic equations},
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Yu. S. Èmanuilov. Controllability of parabolic equations. Sbornik. Mathematics, Tome 186 (1995) no. 6, pp. 879-900. http://geodesic.mathdoc.fr/item/SM_1995_186_6_a5/