I would like to understand what the first paragraph after 3 on page 40 is saying, because I want to understand the set up of the first initial-boundary value problem which follows.
Suppose if we have just x and t and a 2 dimensional problem.
Suppose we take D to be a strip.
$D=[T_1, T_2]\times \Omega$
What would be the $B, B_T, S$ here? Also a more complicated example would also be appreciated.