Counting Ancient Solutions on A Strip with Exponential Growth

2020/08/22 by Gui, Feng
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2008.09855

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.

Related

• Ancient caloric functions and parabolic frequency on graphs
• On ancient solutions of the heat equation
• Dimensional bounds for ancient caloric functions on graphs
• Ancient caloric functions on graphs with unbounded Laplacians
• Time analyticity of ancient solutions to the heat equation on graphs