Jaeger provide many solutions of the heat conduction equation, and Crank 

 (1975) gives solutions to the diffusion equation. 



29. The following paragraphs present a review of previously obtained 

 solutions together with new solutions. The new solutions have been derived 

 either from analogies with heat conduction or through the Laplace transform 

 technique, a short outline for which is given in Appendix A. Carslaw and 

 Jaeger (1959) provide a more comprehensive treatment. In order to present the 

 solutions in an efficient and general format dimensionless variables have been 

 used to a large extent although physical understanding may be obscured by the 

 absence of dimensional quantities. Also, in many cases for which the solution 

 is symmetric with respect to a coordinate axis, the solution for only one side 

 of the symmetry line is displayed. The solutions have been divided into two 

 groups based on the physical properties of the initial and boundary condi- 

 tions, not on their mathematical properties, because the object of the report 

 is to present solutions and not to describe details of their derivation. The 

 first group of solutions describes shoreline change situations without coastal 

 structures. Solutions describing shoreline evolution in these cases are 

 applicable both to natural and artificial beach forms (nourished beaches) if 

 similar types of wave conditions prevail. Also, several solutions describing 

 river delta growth are presented covering the cases of a river discharging 

 sand as a point source and a river mouth of finite length. 



30. The other group of solutions comprises configurations involving 

 various types of coastal structures such as groins, jetties, detached break- 

 waters, and seawalls. Since the equations quickly become complicated, the 

 influence of coastal structures on shoreline evolution has to be idealized to 

 a considerable extent. However, the essential features of the situation may 

 still be preserved if this idealization is carried out in a physically reason- 

 able manner. Some simple models to account for diffraction downdrift of a 

 groin are shown also. 



31. Most of the analytical solutions are presented in the main text 

 without derivation. Reference is made to the appropriate literature in case 

 the reader is interested in deriving the solutions. Also, in Appendixes B-G, 

 derivations are given for selected new solutions. 



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