Time analyticity of ancient solutions to the heat equation on graphs
Fengwen Han, Bobo Hua, Lili Wang
TL;DR
This paper investigates the time analyticity of ancient solutions to heat equations on graphs, establishing conditions under which these solutions are analytic in time, extending prior work to a graph setting.
Contribution
The paper proves the time analyticity of ancient solutions to heat equations on graphs under sharp growth conditions, extending previous results from continuous to discrete structures.
Findings
Ancient solutions are time-analytic on graphs under certain growth conditions.
Established sharp growth conditions for analyticity.
Extended previous continuous domain results to graph settings.
Abstract
We study the time analyticity of ancient solutions to heat equations on graphs. Analogous to Dong and Zhang [DZ19], we prove the time analyticity of ancient solutions on graphs under some sharp growth condition.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Geometric Analysis and Curvature Flows · Advanced Mathematical Modeling in Engineering