Abstract
In this study, we consider a heat transmission problem which has derivative with respect to the time in boundary condition. Applying the seperation of variables method, we get a Sturm-Liouville equation with discontinuous coefficient and a spectral parameter dependent boundary condition. For this spectral problem, the operator theoretic formula is given, the resolvent operator constructed and the expansion formula with respect to the eigenfunctions obtained. Using the expansion formula, the solution of the heat problem expressed.
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