The problem is the BC's i.e. =1 part. If
then so choosing gives
and choosing gives
With solving for gives what you want.
I must solve this initial boundary value problem by transforming it into homogeneous BCs.
---> My work
I set where S(x,t) is the steady state and U(x,t) is the transient
So i substitute s(x,t) into the BCs
These two equations can give us b(t)=1 and a(t)=2/1-h ?
and therefore u(x,t)=2x/(1-h) + (1-x) + U(x,t) = 1 - (1+h/1-h)x + U(x,t)
MY PROBLEM is, how did they get b(t)=1 and a(t) = 2/1-h.
I know i have have to make s(0,t) = to something like a(t) + b(t) = 1 and s_x(1,t) = ?something? so that i can plug it into the but I am not sure what s and s_x should be.
Can someone please tell me what they are so I can finally get a(t) and b(t).
Then I can finally finish solving this problem.
Thanks in advance!