Abstract
It was shown in [4, 14] that a bounded solution of the heat equation in a half-space which becomes zero at some time must be identically zero, even though no assumptions are made on the boundary values of the solutions. In a recent example, Luis Escauriaza showed that this statement fails if the half-space is replaced by cones with opening angle smaller than 90°. Here we show that the result remains true for cones with opening angle larger than 110°.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1414-1429 |
| Number of pages | 16 |
| Journal | Communications in Partial Differential Equations |
| Volume | 37 |
| Issue number | 8 |
| DOIs | |
| State | Published - Aug 2012 |
Bibliographical note
Funding Information:L. L. is supported in part by Louise T. Dosdall fellowship and Doctoral Dissertation Fellowship. V. S. is supported in part by NSF grant DMS 0800908.
Keywords
- Backward uniqueness
- Cone domain
- Heat equation
- Parabolic equations