Involve: A Journal of Mathematics

  • Involve
  • Volume 12, Number 6 (2019), 1015-1034.

Nonstandard existence proofs for reaction diffusion equations

Connor Olson, Marshall Mueller, and Sigurd B. Angenent

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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.

Article information

Involve, Volume 12, Number 6 (2019), 1015-1034.

Received: 19 September 2018
Revised: 28 March 2019
Accepted: 2 April 2019
First available in Project Euclid: 13 August 2019

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26E35: Nonstandard analysis [See also 03H05, 28E05, 54J05] 35K57: Reaction-diffusion equations

nonstandard analysis partial differential equations reaction diffusion equations


Olson, Connor; Mueller, Marshall; Angenent, Sigurd B. Nonstandard existence proofs for reaction diffusion equations. Involve 12 (2019), no. 6, 1015--1034. doi:10.2140/involve.2019.12.1015.

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