A note on time analyticity for ancient solutions of the heat equation
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- by Qi S. Zhang PDF
- Proc. Amer. Math. Soc. 148 (2020), 1665-1670 Request permission
Abstract:
It is well known that generic solutions of the heat equation are not analytic in time in general. Here it is proven that ancient solutions with exponential growth are analytic in time in ${\mathbf {M}} \times (-\infty , 0]$. Here $\mathbf {M}=\mathbf {R^n}$ or is a manifold with Ricci curvature bounded from below. Consequently a necessary and sufficient condition is found on the solvability of the backward heat equation in the class of functions with exponential growth.References
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Additional Information
- Qi S. Zhang
- Affiliation: School of Mathematical Sciences, Fudan University, Shanghai 200433, People’s Republic of China; and Department of Mathematics, University of California, Riverside, California 92521
- MR Author ID: 359866
- Email: qizhang@math.ucr.edu
- Received by editor(s): May 13, 2019
- Received by editor(s) in revised form: August 25, 2019
- Published electronically: November 4, 2019
- Additional Notes: We are grateful to the Simons Foundation for its support through grant No. 282153.
- Communicated by: Guofang Wei
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 1665-1670
- MSC (2010): Primary 35K05, 58J65
- DOI: https://doi.org/10.1090/proc/14830
- MathSciNet review: 4069203