Boundary condition at outlet of channel for diffusion equation

[brambram]

Homework Statement

BOUNDARY CONDITION PROBLEM
I have came up with matrix for numerical solution for a problem where chemical is introduced to channel domain, concentration equation:

δc/δt=D*((δ^2c)/(δx^2))-kc

assuming boundary conditions for c(x,t) as : c(0,t)=1, c(a,t)=0. Where a is channel's length.

What if domain is not-infinite (as it is above) and we cannot assume that the chemical is not dispersed at the end of the channel- so the boundary condition c(a,t)=0 is no longer valid?

Homework Equations

What boundary condition can we use when we cannot assume that the chemical is not dispersed at the outlet of the channel?

 

[haruspex]

Perhaps it is asking you to set c(a, t) = f(t) for some unknown function f and obtain a solution in terms of f. But I'm only guessing.