Mathematical Research Letters

Volume 29 (2022)

Number 5

Counting ancient solutions on a strip with exponential growth

Pages: 1445 – 1459

DOI: https://dx.doi.org/10.4310/MRL.2022.v29.n5.a6

Author

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

Abstract

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