Green's functions for water waves in porous structures

Representations for Green's functions suitable for water-wave problems involving porous structures are obtained by integrating solutions to appropriate heat conduction problems with respect to time. By utilizing different representations for these heat equation solutions for small and large times, the changeover being determined by an arbitrary positive parameter a, a one-parameter family of formulas for the required Green's function is derived and 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 effciency of the resulting formulas.