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Time-dependent singularities in the heat equation

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  • We consider solutions of the heat equation with time-dependent singularities. It is shown that a singularity is removable if it is weaker than the order of the fundamental solution of the Laplace equation. Some examples of non-removable singularities are also given, which show the optimality of the condition for removability.
    Mathematics Subject Classification: Primary: 35K05; Secondary: 35A20, 35B40.

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