Geodesic
Variational methods in nonstationary problems (parabolic case)
Izvestiya. Mathematics , Tome 4 (1970) no. 2, pp. 431-463

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In this paper we present a method for constructing a generalized solution of boundary problems for nonlinear parabolic equations and systems. We assume that the stationary (elliptic) part of these equations is generated by a convex functional. A feature of the scheme we propose is that the construction of the generalized solution can be carried out by using the functional itself without considering its variation. 
@article{IM2_1970_4_2_a9,
     author = {P. P. Mosolov},
     title = {Variational methods in nonstationary problems (parabolic case)},
     journal = {Izvestiya. Mathematics },
     pages = {431--463},
     publisher = {mathdoc},
     volume = {4},
     number = {2},
     year = {1970},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1970_4_2_a9/}
}
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P. P. Mosolov. Variational methods in nonstationary problems (parabolic case). Izvestiya. Mathematics , Tome 4 (1970) no. 2, pp. 431-463. http://geodesic.mathdoc.fr/item/IM2_1970_4_2_a9/