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The divisible sandpile starts with i.i.d. random variables (“masses”) at the vertices of an infinite, vertex-transitive graph, and redistributes mass by a local toppling rule in an attempt to make all...
Asymptotic behavior for the heat equation in nonhomogeneous media with critical density
heat equation non-homogeneous media singular density asymptotic behavior radially symmetric solutions
2012/6/21
We study the asymptotic behavior of solutions to the heat equation in nonhomogeneous media with critical singular density $$ |x|^{-2}\partial_{t}u=\Delta u, \quad \hbox{in} \ \real^N\times(0,\infty). ...