We study asymptotic solutions of a Cauchy problem for induction equations describing magnetic field in a well conducting fluid. We assume that the coefficient (the velocity field of the fluid) changes rapidly in a small vicinity of a two- dimensional surface. We prove that the weak limit of the solution has delta-type singularity on this surface; in the case of a perfectly conducting fluid, we describe several regularizations of the problem with discontinuous coefficients which allow to define generalized solutions.

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