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.
© 2016 by De Gruyter