We consider smooth solutions to the biharmonic heat equation on ℝn x [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.
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Simon, M. & Wheeler, G. (2016). Some local estimates and a uniqueness result for the entire biharmonic heat equation. Advances in Calculus of Variations, 9 (1), 77-99.