D. E. Panayotounakos, K. P. Zafeiropoulos, "General solutions of the nonlinear PDEs governing the erosion kinetics", Mathematical Problems in Engineering, vol. 8, Article ID 239581, 17 pages, 2002. https://doi.org/10.1080/10241230211379
General solutions of the nonlinear PDEs governing the erosion kinetics
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.
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