Singular solutions of a two-phase problem for the parabolic equations with a time derivative in the conjugation conditionsunder the incompatibility of the initial and boundary data

A two-phase problem for the heat equations with the time derivative in the conjugation conditions is studied under the incompatibility of the initial and boundary data. Singular solutions of the problem are constructed in explicit form. Such solutions appear due to the nonfulfillment of the compatibility conditions. We prove that the solution of the problem is the sum of a Hölder function and singular functions whose number is equal to the number of incompatibilities of the given functions at the boundary of the domain.