[Edwards-Wilkinson equation] solving inhomogeneous heat equation

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During studying kinetic view Chap2.9 Application to surface growth

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The solution of above inhomogeneous heat equation can be written as follows:

Here, eta is an inhomogeneous term and the following is the heat kernel (Green function involved in convolution).

That is, a noise input at (x1,t1) propagates to (x,t) via the Gaussian propagator of diffusion. 

The eta which acts at time t1 on x1 will propagate and affect to height at position x at time t, and this is formulated as above with the Gaussian propagator.

[ref] https://en.wikipedia.org/wiki/Heat_equation#Inhomogeneous_heat_equation

Eq. (2.109) is more easily solved by using Fourier transform, because the Fourier transforms of Gaussian and white noise are Gaussian and constant, respectively.