Some local estimates and a uniqueness result for the entire biharmonic heat equation
classification
🧮 math.AP
keywords
estimatessolutionsbiharmonicequationheatlocalsmoothsome
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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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