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Licensed Unlicensed Requires Authentication Published by De Gruyter December 4, 2014

Some local estimates and a uniqueness result for the entire biharmonic heat equation

  • Miles Simon EMAIL logo and Glen Wheeler

Abstract

We consider smooth solutions to the biharmonic heat equation on ℝn × [0,T] for which the square of the Laplacian at time t is globally bounded from above by k0/t for some k0 in ℝ+, for all t ∈ [0,T]. We prove local, in space and time, estimates for such solutions. We explain how these estimates imply uniqueness of smooth solutions in this class.

Funding source: Alexander-von-Humboldt Foundation

Award Identifier / Grant number: 1137814

Funding source: Australian Research Council Discovery Project

Award Identifier / Grant number: DP120100097

Funding source: University of Wollongong Research Council

Award Identifier / Grant number: 2014 Small Grant 228381024

The first author would like to thank the University of Wollongong, where part of this work was carried out.

Received: 2014-8-5
Revised: 2014-10-19
Accepted: 2014-10-22
Published Online: 2014-12-4
Published in Print: 2016-1-1

© 2016 by De Gruyter

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