Using "Limit" when the limit is a delta function

*To*: mathgroup at smc.vnet.net*Subject*: [mg85199] Using "Limit" when the limit is a delta function*From*: Jim Rockford <jim.rockford1 at gmail.com>*Date*: Fri, 1 Feb 2008 02:20:34 -0500 (EST)

I'm just wondering whether I can get Mathematica to understand the following limit (I'm using version 6.01). The standard solution for u(x,t) of the diffusion equation u_t = D u_xx over an infinite domain with initial condition u(x,0) = delta(x) (Dirac delta) is u[x_,t_] = (1/Sqrt[4 Pi D t]) Exp[-x^2/(4 D t)] This solution, in fact, defines a family of functions whose limit as t-->0 yields the Dirac delta, as the initial condition dictates. In Mathematica I tried Limit[u[x, t], t -> 0] and got nothing from it. Can I get Mathematica to handle this sort of limit? I realize that it involves an essential singularity at t=0, but I would've guessed that Mathematica is equipped to deal with it. An extra option needs to be specified or something? Thanks, Jim