The PDE: ∂n/∂t + G∂n/∂L=0
The initial condition: n(0,L)=ns
The boundary condition: n(t,0)=B/G
The parameter B and G above are dependent upon process conditions and change at each time. They can be calculated with adequate experimental data.
I know that the characteristic equations for this PDE are:
Solving the above:
The Attempt at a Solution
From what I can see, the above equations suggest that along a characteristic curve given by equation (6), the population density, n, at size L0, travels along the size axis with rate of growth, G.
The initial condition, n(0,L)=ns describes the population of particles over a given size range. So the initial data I have is a number of values of population density, n, at a number of sizes.
Does the solution suggest that each initial value of population density, n corresponding to an initial size, L0 will stay constant along equation (6) and correspond to a different size in the next time step???? I hope I am clear in what im saying here.