# Heat equation

1. May 7, 2010

### squenshl

I got a solution to the heat equation using Fourier transforms with the special case g(x) = GH(x-a)
u(x,t) = G/2[1+erf(x-a/(2$$\sqrt{t}$$))]. But I just wanted to know what this special case represents physically.
I should probably ask what does any special case to the heat equation represent physically.

2. May 9, 2010

### elibj123

I guess H(x-a) is a shifted heaviside function.
So what it represents is a piece of matter which at initial state is divided into two sections- one with tempretare G, the second with zero. Physically you can create this by taking two pieces of heat conducting matter, cooling one to almost absolute zero (or what ever relative zero you use), the second you heat to a certain temprature, and then putting them together, then watch how heat transfers along the medium. (I guess you can have better methods)

In general, heat equation studies diffusive motion. It doesn't have to deal with heat at all. You'll have the same equation for free charges in a conducting device. You can also develope a model of a uniform random walk, in which your probability density function changes in time, and again obtain the same equation.