Green's functions for water waves in porous structures

Representations for Green's functions suitable for water-wave problems invo lving porous structures are obtained by integrating solutions to appropriat e heat conduction problems with respect to time. By utilizing different rep resentations for these heat equation solutions for small and large times, t he changeover being determined by an arbitrary positive parameter a, a one- parameter family of formulas for the required Green's function is derived a nd by varying a the convergence characteristics of this new representation can be altered. Letting a --> 0 results in known eigenfunction expansions. The results of computations are presented showing the accuracy and efficien cy of the resulting formulas. (C) 2000 Elsevier Science Ltd. All rights res erved.