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On representation of solutions to the heat equation
Published 30 Oct 2023 in math.AP and math.CA | (2310.19330v1)
Abstract: We propose a simple method to obtain semigroup representation of solutions to the heat equation using a local $L2$ condition with prescribed growth and a boundedness condition within tempered distributions. This applies to many functional settings and, as an example, we consider the Koch and Tataru space related to $BMO{-1}$ initial data.
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