科研之友
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摘要
We study a porous medium equation with nonlocal diffusion effects given by an inverse fractional Laplacian operator: partial derivative(t)u - del . (u del p) = 0, p = (-Delta)(-s) u, 0 < s < 1. We pose the problem for x is an element of R(n) and t > 0 with bounded and compactly supported initial data, and prove the existence of weak and bounded solutions that propagate with finite speed, a property that is not shared by other fractional diffusion models.
- 出版日期2011-11
