Initial-boundary value problems for parabolic equations of the second order can be formulated, like the elliptic problems, also by means of conjugate variables, i.e. in terms of the cogradient vector function.
The conjugate problem is shown to belong to a class of abstract parabolic equations with two positive operators, which have been analysed in a previous author's paper. The first and second semi-variational approximations to the solution of the conjugate problem are presented together with some error estimates.
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