This article is available for purchase or by subscription. See below.
Abstract
|
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.
|
\vrule height 2.5pt depth -2pt width
26pt To the memory of Terry Millar \vrule height 2.5pt depth
-2pt width 26pt
|
PDF Access Denied
However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/involve
We have not been able to recognize your IP address
18.206.177.17
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for
USD 30.00:
Keywords
nonstandard analysis, partial differential equations,
reaction diffusion equations
|
Mathematical Subject Classification 2010
Primary: 26E35, 35K57
|
Milestones
Received: 19 September 2018
Revised: 28 March 2019
Accepted: 2 April 2019
Published: 3 August 2019
Communicated by Suzanne Lenhart
|
|