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Mathematical Problems in Engineering
Volume 8, Issue 1, Pages 69-85
http://dx.doi.org/10.1080/10241230211379

General solutions of the nonlinear PDEs governing the erosion kinetics

Division of Mechanics, Department of Applied Sciences, National Technical University of Athens, Hellas, Greece

Received 13 July 2001

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We present the construction of the general solutions concerning the one-dimensional (1D) fully dynamic nonlinear partial differential equations (PDEs), for the erosion kinetics. After an uncoupling procedure of the above mentioned equations a second–order nonlinear PDE of the Monge type governing the porosity is derived, the general solution of which is constructed in the sense that a full complement of arbitrary functions (as many as the order) is introduced. Afterwards, we specify the above solution according to convenient initial conditions.