Hello all,
I am trying to implement a system of Partial Differential Equations. i am using the PDE Toolbox which seems quite complete.
The 2-D system is the following :
dn/dt + nabla * (nv) = 0 [1]
dv/dt + v * nabla v = nabla c [2]
dc/dt = D nabla^2 c + alpha n - c/tau [3]
Where the variables are n, v and c, and depend on x,y and t. The derivatives are of course partial ones. alpha, tau and D are parameters. Variable v is a vector.
This system comes from a scientific article, and the following indications are given :
[1] is a mass conservation equation
[2] is a Burgers equation
[3] is a reaction-diffusion equation
The main problem I have is that [3] is the only equation I managed to get in shape for the PDE toolbox to be able to solve.
Indeed, the form that the toolbox takes is : d * du/dt nabla·(nabla c u)+au=f, where d, c, a and f are coefficients which may depend on u, du/dx, du/dy, x and y.
I cannot manage to see how to write [1] and [2] in this form, especially for the second term.
This makes me think that perhaps I am considering the problem all wrong. These PDEs seem quite different to me, and maybe I'm not taking the right approach by trying to jumble them all together.
Any help on how to get started on implementing this would be a great help.
Thank you in advance, Clément
