Solving PDEs problem by Green function usually with homogeneous and inhomogeneous initial condition, so how to deal with first order derivative inhomogeneous initial condition?
Thank you, for your reply, and I have attached the PDEs Eq which might make the question clear.....
Dear Azzam, I checked your equation, which is a 1D diffusion equation (Parabolic DE), and its Greens fct is very well known, and it can be obtained easily from the point source solution of DE, as follows:
G(x,t) = M /2 (Pi Kappa t)1/2 * exp[- x2 / 4 Kappa t ],
The Integral of G(x,t) dx from minus infinity to plus infinity is equal to M.
For 3D one has: G(r,t) = M/ 8 (Pi Kappa t)3/2 * exp[- r2 / 4 Kappa t ],
Where Kappa is a constant (Diffusivity or thermal conductivity), M is the total amount of substance diffusion or the intensity of the point source.
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