Consider the heat equation in a three-dimensional

Question

1. Consider the heat equation in a three-dimensional box-shaped region.

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ðu/ðt= k(ð²u/ðx²+ð²u/ðy²+ð²u/ðz²)

Subject to the initial condition u(x,y,z,0)= f(x,y,z).

2. Solve the initial value problem and analyse the temperature as t--> infinity if the boundary conditions are

u(0,y,z,t)=0,   ðu/ðy(x,0,z,t)=0,  ðu/ðz(x,y,0,t)= 0,

u(L,y,z,t)=0,   ðu/ðy(x,H,z,t)=0,  u(x,y,W,t)=0

It looks like the problems are marked out, but they are not—it is a used book.

I need the 3-D heat equation with parts a and b completed, please