Recovery of a variable coefficient in a coastal evolution equation

A method is presented for reconstructing an unknown coefficient in a linear diffusion equation from measured data. This equation arises in the descrip tion of coastline evolution, and preliminary results are presented here. Th e unknown term may vary with both space and time, although time variation i s assumed to be slow. Inversion is carried out by first expressing the solu tion of the direct problem formally in terms of the governing operators and making explicit approximations to these expressions. Using data at two tim e steps this then allows equations to be derived and solved to give explici t expressions for the required function. (C) 1999 Academic Press.