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Spatial Decay Estimates and Continuous Dependence on Modelling for an Equation from Dynamo Theory

F. Franchi and B. Straughan
Proceedings: Mathematical and Physical Sciences
Vol. 445, No. 1924 (May 9, 1994), pp. 437-451
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/52607
Page Count: 15
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Spatial Decay Estimates and Continuous Dependence on Modelling for an Equation from Dynamo Theory
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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 Holder continuously on changes in the prescribed velocity field.

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