I'm not sure how to solve this:
du/dt = 3 \frac{d^{2}u}{dx^{2}}
These are the conditions:
u(0,t)= -1
u(pi,t)= 1
u(x,0) = -cos 7x
Suggestion:
I should use steady state solution to get a homogeneous initial condition.
Starting with separtion of variables
u(x,t) = G(x)H(t)
And...
Y ⊂ X where X is a metric space with the function d. Prove that (Y,d) is a metric space with the same function d.
The metric function d: X x X -> R.
I know that the function for Y is:
d* : Y x Y -> R
How do I show that d is the same as d*.