Abstract
This paper studies the improperly posed, backward in time problem, in addition to the well posed forward in time problem, for a non-symmetric partial differential equation which describes the behaviour of the toroidal part of the magnetic field in a dynamo problem. We first show that solutions in an unbounded cylinder decay exponentially in space provided that for the backward in time problem a Dirichlet integral is bounded and provided the prescribed velocity field satisfies particular bounds; for the forward in time problem several of these constraints are relaxed. It is next shown that the solution to the same problem on a bounded spatial domain depends Hölder continuously on changes in the prescribed velocity field.
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