ABSTRACT. We study the asyanptotics of solutions to the Dirichlet problem for the heat equation in timedependent domains with singular points.

We study solutions of the Dirichlet problem for a second-order parabolic equation with variable coefficients in domains with nonsmooth lateral surface. The asymptotic expansion of the solution in powers of the parabolic distance is obtained in a neighborhood of a singular point of the boundary. The exponents in this expansion are poles of the resolvent of an operator pencil associated with the model problem obtained by ~freezing" the coefficients at the singular point. The main point of the paper is in proving that the re.solvent is meromorphic and in estimating it. In the one-dimensional case, the poles of the resolvent satisfy a transcendental equation and can be expressed via parabolic cylinder functions.

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