We give an existence proof for distribution solutions to a scalar reaction
diffusion equation, with the aim of illustrating both the differences and
the common ingredients of the nonstandard and standard approaches. In
particular, our proof shows how the operation of taking the standard part
of a nonstandard real number can replace several different compactness
theorems, such as Ascoli’s theorem and the Banach–Alaoglu theorem on
weak-compactness
of the unit ball in the dual of a Banach space.
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26pt To the memory of Terry Millar \vrule height 2.5pt depth
-2pt width 26pt