الفهرس 
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Abstract
coastal processes associated with the shoreline evolution are highly complex and the mathematical modelling of these processes have received limited attention in the past[1].Inspite of these difficulties, a reasonable estimate of the long-term shoreline evolution by making a mathematical model would be useful .In this thesis a mathematical model which calculates the wave characteristics such as wave direction wave height and the wave velocity in successive points in the shallow water and the breaking area along the orthognal rays by knowing the wave characteristics in the deep water and the contours map of the used area.Numerical results are obtained for 80 km from rossetta coast and are used for as input to the following part. this thesis concerns with areas characterized by longshore sediment transport only thus groin system can be effectively used in general with least expenses to get stable shoreline .
Also in this thesis a mathematical model which solves the problems of maximizing the acquired area in the case of stable shoreline or minimizing the least square error between the present shoreline and the shoreline after oneyear in the case of unstable shoreline with respect to the groin dimension and the space between them.