We study the boundary-value problem of determining the parameter p of a parabolic equation v'(t) + Av(t) = f(t) + p, 0 <= t <= 1, v(0) = phi, v(1) = psi, with strongly positive operator A in an arbitrary Banach space E: The exact estimates are established for the solution of this problem in Holder norms. In applications, the exact estimates are obtained for the solutions of the boundary-value problems for parabolic equations.
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