On the problem of determining the parameter of a parabolic equation

Abstract

We study the boundary-value problem of determining the parameter p of a parabolic equation $$v′(t)+Av(t)=f(t)+p,\;0⩽t⩽1,v(0)=φ,\;v(1)=ψ,$$ with strongly positive operator $A$ in an arbitrary Banach space $E$. The exact estimates are established for the solution of this problem in Hölder norms. In applications, the exact estimates are obtained for the solutions of the boundary-value problems for parabolic equations.