Fractional heat equation

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(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...")
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where $(-\Delta)^s$ stands for the [[fractional Laplacian]].
where $(-\Delta)^s$ stands for the [[fractional Laplacian]].
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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.
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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.

Revision as of 21:38, 8 June 2011

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.

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