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We analyse the behaviour of solutions of the linear heat equation in Rd for initial data in the classes Mε(Rd) of Radon measures with ∫Rde−ε|x|2d|u0|<∞. We show that these classes are optimal for local and global existence of non-negative solutions: in particular M0(Rd):=∩ε>0Mε(Rd) consists of those initial data for which a solution of the heat equation can be given for all time using the heat...
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