Standard PDE: solution wanted.
- To: mathgroup at smc.vnet.net
- Subject: [mg42464] Standard PDE: solution wanted.
- From: "kl" <klimm1290 at yahoo.com>
- Date: Thu, 10 Jul 2003 03:36:49 -0400 (EDT)
- Organization: Purdue University
- Sender: owner-wri-mathgroup at wolfram.com
I am trying to solve the following PDE which is a form of diffusion equation. d/dt(rho) = div [D*grad(rho)] + r Assume D to be constant r is constant rho is the only dependent variable and depends on space coordinates and time. As it can be seen, it is a very common equation and similar equation with appropriate change in parameters can be found in heat conduction problems in solids. I am trying to solve this equation in 2D Cartesian coordinate system. My domain is a rectangle of length L and height H. Hence my equation becomes - d/dt(rho) = D*d2/dx2(rho) + D*d2/dy2(rho) + r Initial condition for this problem is - All over the domain, rho is known and constant at time t = 0 (you can call it rho_init) Boundary conditions for this problem are - Top surface is open and hence rho = rho_init at that surface for all times t Other three surfaces are impermeable and hence grad(rho) = d/dx(rho) + d/dy(rho) = 0 Can anyone tell me how to find this solution of the problem using mathematica? Do anyone know of an analytical solution to this problem? - If so please direct me to the book where I can find that solution. (I am pretty sure that analytical solution exists, I am just not being able to find it)