A New Approach to 'Queer' Differential Equations.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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Queer differential equations first arose in the work of Harold Grad on controlled thermonuclear fusion. These relate in particular to models for the slow adiabatic evolution and resistive diffusion of a plasma. These are queer in that these share aspects of partial, ordinary and functional differential equations. In this document the authors give a new way of thinking of these equations by relating these to free boundary problems. This is the first of a series of papers intending to demonstrate that solutions of such a queer differential equation can be thought of as limits of solutions of free boundary problems with n-free boundaries. A long term hope is that this work will complement and further refine existing numerical schemes for finding such solutions.
- Theoretical Mathematics