Finite domain (Dirichlet problem)

The simplest finite domain in a one-dimensional space is a segment of length $L$, namely $x \in [0,L]$. As a practical reference case, you may imagine that the territory is an island or a wood which is very narrow, oblong and of length $L$ (see Fig. 3A), and the habitats outside the island or the forest are totally unsuitable for the survival and movement of the dispersing organisms. Then the boundary conditions become

$$c(0,t) = c(L,t) = 0.$$

In mathematical terms this problem is often called absorbing barrier problem.