Talk:Perturbation methods and Nonlocal porous medium equation: Difference between pages
(Difference between pages)
imported>Luis (Created page with "The note on '''perturbation methods''' is difficult to write. It is hard not to make the concept sound very vague. I don't know how much detail should be given in the examples ei...") |
imported>Nestor (Created page with "The nonlocal porous medium equation of order $\sigma$ is the name currently given to two very different equations, namely \[ u_t = \nabla \cdot \left ( u \nabla \mathcal{K_\alph...") |
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The | The nonlocal porous medium equation of order $\sigma$ is the name currently given to two very different equations, namely | ||
\[ u_t = \nabla \cdot \left ( u \nabla \mathcal{K_\alpha} (u) \right )\] | |||
\[\mbox{ where } \mathcal{K}_\alpha(u) := C_{n,\alpha}\; u * |x|^{-n+\alpha},\;\; \alpha+2=\sigma \] | |||
and | |||
\[ u_t +(-\Delta)^{s}(u^m) = 0 \] | |||
These equations agree when $s=1$ and $m=2$. They are fractional order [[Quasilinear equations]]. | |||
Revision as of 00:37, 2 June 2011
The nonlocal porous medium equation of order $\sigma$ is the name currently given to two very different equations, namely
\[ u_t = \nabla \cdot \left ( u \nabla \mathcal{K_\alpha} (u) \right )\]
\[\mbox{ where } \mathcal{K}_\alpha(u) := C_{n,\alpha}\; u * |x|^{-n+\alpha},\;\; \alpha+2=\sigma \]
and
\[ u_t +(-\Delta)^{s}(u^m) = 0 \]
These equations agree when $s=1$ and $m=2$. They are fractional order Quasilinear equations.