Dear Sir/Madam;
I am looking for an advise on a reference that gives a 1D Nonlinear Reaction Diffusion Equation Initial Value Problem, and if possible describes a real life application.
Many thanks
Best regards
Sarmad.
The following are two references in the topic
http://booksc.org/book/18618413/08646b
http://booksc.org/book/27344452/88259c
The following are two references in the topic
http://booksc.org/book/18618413/08646b
http://booksc.org/book/27344452/88259c
I have attached PDFs of two Mathematica notebooks that describe the analysis of nonlinear reaction diffusion problems. One deals with the Fisher Equation, the other deals with a nonlinear predator-prey problem. These are classical problems that are often presented in graduate classes on bifurcation analysis of reactor diffusion problems. If needed you can download the Mathematica files from the following site: https://sites.google.com/site/chemengwithmathematica/ . Check the section on Bifurcation Analysis for the downloaded files. Hope this provides some input to your question.
One of the best introductions to the problem of the reaction-diffusion equation in simple geometry, including a real life applications, is presented by Kuttler (2011), "Reaction-diffusion equations with applications", the text is available at:
http://www-m6.ma.tum.de/~kuttler/script_reaktdiff.pdf
Despite the fact that considerations are made in a one dimensional space, the effective dimensionality of the problem is (n + 1), where n is the number of interacting elements.
For the general introduction to this subject, I suggest to consult the seminal article of Turing (1952): The Chemical Basis of Morphogenesis, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, Vol. 237, No. 641. (Aug. 14, 1952), pp. 37-72.
The texts is posted at:
http://www.dna.caltech.edu/courses/cs191/paperscs191/turing.pdf
or alternatively at:
http://links.jstor.org/sici?sici=0080-4622%2819520814%29237%3A641%3C37%3ATCBOM%3E2.0.CO%3B2-I
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