Nonlinear Degenerate Diffusion Problems
نویسندگان
چکیده
Self similar solutions u(x,t) = f(x//t) of the one-dimensional porousmedium equation are studied in this paper. These solutions emerge frominitial values that consist of two constant states: one non-positive forx < 0 and one non-negative for x > 0. With a diffusivity of the form|u| , we consider for m > 0 sign change solutions and for m e (-1,0]non-negative solutions. The method we use is based on a transformationwhich maps the ordinary differential equation for f into a singular ellipticboundary value problem with Dirichlet conditions.Special attention is given to the behaviour of f near zero. We also presenta number of numerical results. 138
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تاریخ انتشار 2007