HR: 14:35h
AN: H22G-04    [PDF]
TI: Analytical Solutions Of The Degenerate Diffusion Equation
AU: Salomon, J B
EM:
AF: The University of Mississippi, Department of Civil Engineering, University, MS 38677 United States
AU: Prasad, S N
EM: cvprasad@olemiss.edu
AF: The University of Mississippi, Department of Civil Engineering, University, MS 38677 United States
AU: * R”mkens, M J
EM: mromkens@ars.usda.gov
AF: USDA-ARS-NSL, 598 McElroy Drive, Oxford, MS 38655 United States
AB: Certain nonlinear diffusion equations of degenerate parabolic type display a finite speed of propagation of disturbances. This mathematical behavior can be used to describe a wide range of nonlinear phenomena such as the penetration distance of a thermal layer, the boundary of a reaction zone, or a wetting front unsaturated soil moisture flow. However there are two maindifficulties in obtaining solutions to problems of this class. One is that the location of the interface is not known a priori and must be discovered during the analysis. The other is the fact that the differential equation is singular in the neighborhood of the interface. The solution technique developed and presented in this work overcomes these difficulties by extracting a local solution of the differential equation in the neighborhood of the diffusing front. One profound result is the discovery that the velocity of the front is entirely controlled by the first term of the spectral series expansion. Also, by capturing the critical behavior of the solution in the region of the singularity and incorporating the behavior as a dominant factor, the series expansion is provided a means for very rapid convergence. The versatility of the solution technique is demonstrated by solving various boundary value problems covering a broad range of interest and the solutions are tested against previously published results.
DE: 1860 Runoff and streamflow
DE: 1866 Soil moisture
DE: 1875 Unsaturated zone
SC: Hydrology [H]
MN: 2003 Fall Meeting