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Blow-up for the heat equation with a general memory boundary condition

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  • In this paper, we study the long-time behavior of nonnegative solutions of the heat equation with a general memory boundary condition. We first present conditions on the memory term for finite time blow-up. We then establish global existence results through both analytical and numerical methods. Finally, we show that under certain conditions blow-up occurs only on the boundary.
    Mathematics Subject Classification: Primary: 35B44, 35K05, 35K20.


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