Effects of errors in the initial-time geometry on the solution of an equation from dynamo theory in an exterior domain

Abstract

This paper studies the improperly posed backward-in-time problem, in addition to the forward-in-time problem, for a solution to a non-symmetric partial differential equation which arises in dynamo theory. Throughout, the spatial domain is unbounded and exterior to a compact region in three-space. Continuous dependence on changes in the initial-time geometry is established. For the forward-in-time problem, an explicit continuous dependence inequality depending solely on data is derived, while for the backward-in-time problem, a similar inequality is established but the bound depends also on a constraint set.