Nonlinear diffusion in an inhomogeneous aquifer
نویسندگان
چکیده
A selection of these reports is available in PostScript form at the Faculty's anonymous ftp-Abstract We study the large-time behaviour and the behaviour of the interfaces of the nonlinear diiusion equation (x)u t = A(u) in one and two space dimensions. The function A is of porous media type, smooth but with a vanishing derivative at some values of u, and > 0 is supposed continuous and bounded from above. If is not bounded away from zero, the large-time behaviour of solutions and their interfaces can be essentially diierent from the case when is constant. We extend results by Kamin and Rosenau ((13], 14]) and derive the large-time asymptotic behaviour of solutions, as well as a precise characterisation of the behaviour of the interfaces of solutions in one space dimension and in some cases in two space dimensions. In one space dimension and when is monotonic the result states that the interface (t) = supfx 2 R : u(x; t) > 0g tends to innnity in nite time if and only if R 1 0 xx(x) dx < 1.
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تاریخ انتشار 1995