Hi, this is the question
u_t=u_xx 0<x<l, t>0 for u(x,t)
with boundary conditions u(0,t) = f(t) and u(l,t) = g(t) for t>0
and initial condition u(x,0) = h(x) for 0<x<l.
Show that this problem can be transformed into a new equations problem with a new dependent varaible v(x,t) with a 2nd order partial differential equation, vanishing boundary conditions (v(0,t) = v(l,t) = 0, t>0) and an initial condition.
Assume differentiability when needed, f and g are defined for all t needed.
The main problem I have with this question is I'm not sure how to make the boundary conditions vanish...