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Abstract
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In this paper, we consider some initial-boundary value problems which contain one-dimensional heat
equation in non-classical case. For this problem, we can not use the classical methods such as Fourier,
Laplace transformation and Fourier-Birkho methods. Because the eigenvalues of their spectral prob-
lems are not strictly and they are repeated or we have no eigenvalue. The presentation of the solution
and also satisfying the solution in the given P.D.E and satis ng the given initial and boundary con-
ditions are established by complex analysis theory and Countour integral method.
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