Counting ancient solutions on a strip with exponential growth

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.

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Received 31 August 2020

Accepted 4 March 2021

Published 21 April 2023