Fractional heat equation

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 Revision as of 06:28, 8 June 2011 (view source)Luis (Talk | contribs) (Created page with "The fractional heat equation refers to the parabolic equation $u_t + (-\Delta)^s u = 0,$ where $(-\Delta)^s$ stands for the fractional Laplacian. In principle one could s...")← Older edit Revision as of 21:38, 8 June 2011 (view source)Nestor (Talk | contribs) mNewer edit → Line 3: Line 3: where $(-\Delta)^s$ stands for the [[fractional Laplacian]]. where $(-\Delta)^s$ stands for the [[fractional Laplacian]]. - In principle one could study the equation for any value of $s$. The values in the range $s \in (0,2]$ are particularly interesting because in that range the equation has a maximum principle. + In principle one could study the equation for any value of $s$. The values in the range $s \in (0,1]$ are particularly interesting because in that range the equation has a maximum principle.
The fractional heat equation refers to the parabolic equation $u_t + (-\Delta)^s u = 0,$ where $(-\Delta)^s$ stands for the fractional Laplacian.
In principle one could study the equation for any value of $s$. The values in the range $s \in (0,1]$ are particularly interesting because in that range the equation has a maximum principle.