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arXiv · 1405.6813

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

Miles Simon·Glen Wheeler
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Abstract

We consider smooth solutions to the biharmonic heat equation on Euclidean space for which the square of the Laplacian at time t is globally bounded from above by k/t for some k in R, for all t in [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.

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Miles Simon, Glen Wheeler. 2014-05-27. Some local estimates and a uniqueness result for the entire biharmonic heat equation. https://arxiv.org/abs/1405.6813

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