Mathematical Research Letters

Volume 29 (2022)

Number 5

Counting ancient solutions on a strip with exponential growth

Pages: 1445 – 1459



Feng Gui (Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Mass., U.S.A.)


We study the ancient solutions of parabolic equations on an infinite strip. We show that any polynomial growth ancient solution for a class of parabolic equations must be constant. Furthermore, we show that the vector space of ancient solutions that grow slower than a fixed exponential order is of finite dimension.

The full text of this article is unavailable through your IP address:

Received 31 August 2020

Accepted 4 March 2021

Published 21 April 2023