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

2014/05/27 by Miles Simon, Simon, Miles, Glen Wheeler +1
Computer Science · Mathematics · #35B45 #35K25 #35K35 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1405.6813

openalex publication_date 2014/05/27 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

We consider smooth solutions to the biharmonic heat equation on Euclidean\nspace for which the square of the Laplacian at time t is globally bounded from\nabove by k/t for some k in R, for all t in [0,T]. We prove local, in space and\ntime, estimates for such solutions. We explain how these estimates imply\nuniqueness of smooth solutions in this class.\n

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