In this paper, an inverse problem of determining a nonlinear source term in a heat equation with boundary-value condition u x (0, t) = F (t, u(0, t)) is investigated. At first, the problem is equally reduced to a group of integral equations; and secondly, using Sobolev compact imbedding theorem and some skills of integral estimate, the source term's existence in Hölder space is proven by constructing iterative sequences. Finally, uniqueness is obtained in C 0,α (0 < α < 1) space by fixed point theorem and some norm inequalities.
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