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- W2077713045 abstract "We construct two-dimensional polynomial solutions of the fourth-order nonlinear diffusion equation ut+∇·(u∇∇2u)=0. The interfaces and contour lines are given by quadratic curves: ellipses, hyperbolas, and parabolas. The solution with elliptical interfaces represents the spreading of an scalar initially concentrated along a segment. For the cases of the parabolic and hyperbolic interfaces, self-similar solutions are obtained. These solutions may be extended to three and higher dimensions. Some other extensions are also noted." @default.
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- W2077713045 date "2003-03-01" @default.
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- W2077713045 title "Explicit solutions of a two-dimensional fourth-order nonlinear diffusion equation" @default.
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- W2077713045 doi "https://doi.org/10.1016/s0895-7177(03)00015-3" @default.
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