We prove solvability of boundary value problems for forward-backward parabolic equations with a full matrix of gluing conditions. As is known, in the case of forward-backward equations the smoothness of initial and boundary data does not ensure Hölder smoothness of solutions. It is shown that the Hölder classes of solutions to boundary value problem for forward-backward parabolic equations and the number of solvability conditions depend on the matrix of gluing (conjugation) conditions.

Topics
Algebraic geometry
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2018
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