Extended models of sedimentation in coastal zone

Construction of a generalized hyperbolic model of sediment dynamics predicting a sediment evolution on the bottom surface with a finite velocity is presented. The transport equation is extended with introducing a generalized operator of flux change and a generalized operator of gradient. Passing to the convenient model is a singular degeneration of extended model. In this case the results are obtained in the class of generalization solutions. Some expressive examples of constructions of hyperbolic models predicting a finite velocity of disturbance propagation are presented. This problem is developed starting from Maxwell (1861). His approach in the theory of electromagnetism and the kinetic theory of gases is commented. A brief review on propagation of heat and diffusive waves is presented. The similar problems in the theory of probability and diffusion waves are considered. In particular, it was shown on the microscopic level for metals that the conservation law can be violated.