Dear Sarmad, a real life application of reaction-diffusion (system of) equations is pattern morphogenesis studied by A. Turing, see reference.

Gianluca

http://cba.mit.edu/events/03.11.ASE/docs/Turing.pdf

Dear Sarmad,

The propagation of the electrical signal in the heart can be modelled by the monodomain equation, which is a simplification of the more accurate bidomain equations. This simplification is usually made for computational purposes. The monodomain equation is a reaction-diffusion partial differential equation.

A derivation of the monodomain equation can be found on http://www.uio.no/studier/emner/matnat/ifi/INF5610/h07/undervisningsmateriale/review_part6.pdf . I have had a quick look and it seems this derivation is clear.

Best,

Max

Dear Sarmad Jameel,

Reaction-diffusion equation have been applied in many areas of specialization for example, in developmental biology (Ref Alan Turing Work), neuroscience (Ref Hodgkin-Huxley work on Action Potential Propagation), Calcium dynamics (Ref James Sneyd)

Regards,

Hammed

There are many examples from invasion biology:

http://www.reabic.net/publ/Andow_etal_1990.pdf

Dear Professor Sarmad:

Two more examples, one to finance mathematics and another to mathematics applied to biology:

Article A Nonlinear Option Pricing Model Through the Adomian Decompo...

Article Applying Adomian Decomposition Method to Solve Burgess Equat...

Regards,

Oswaldo