Separation of variables ansatz \(c(x,t)=v(x)w(t)\) leads to the eigenvalue problem, see the arguments of Section 4.5, Assume the initial concentration \(c_0(x_1,x_2,x_3)\) of the substrate in a soluti...Separation of variables ansatz \(c(x,t)=v(x)w(t)\) leads to the eigenvalue problem, see the arguments of Section 4.5, Assume the initial concentration \(c_0(x_1,x_2,x_3)\) of the substrate in a solution is constant if \(x_3=const.\) It follows from a uniqueness result below that the solution of the initial-boundary value problem \(c(x_1,x_2,x_3,t)\) is independent of \(x_1\) and \(x_2\).
