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Cauchy problem PDE NDSolve


I am trying to solve a parabolic PDE of a Fokker-Plank type that describes
time evolution of a Gaussian peak in infinite space with NDSolve (Math 3.0).
Obviously, infinite space is the problem, and NDSolve generates something
weird.  I played with the NDSolve parameters and various transformations,
but it didn't help (though the equation coefficients are good smooth
functions).  Does anybody know a Mathematica program/package for a Cauchy
parabolic (diffusion-type) PDE problem in infinite space (asymptotically
vanishing boundary conditions)?  I hope it should exist because NDSolve in
the present form fails to solve even a textbook problem of the diffusion
evolution of a Gaussian peak if the diffusion coefficient changes slightly
in space (it generates some mesh-dependent crap).

Thanks!
Eugene





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