The inverse problem for diffusion equations

In the standard procedure one has to find the concentration from given initial (and boundary) conditions. We investigate here an inverse problem: to find the initial concentration from the known resulting concentration. This problem is of importance particularly for non-linear diffusion equations where the concentration dependenceD D(c) of the diffusion coefficient is analysed in terms of the Boltzmann-like solutionc f(xt^–1/2). This type of solution is, however, closely related to a very special initial condition for the concentration. The disregard of this fact might lead to misleading analysis ofD(c).