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Asymptotic stability and blow-up of solutions for semi-linear edge-degenerate parabolic equations with singular potentials

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  • This article studies the initial boundary value problem for a class of semilinear edge-degenerate parabolic equations with singular potential term. By introducing a family of potential wells, we derive a threshold of the existence of global solutions with exponential decay, and the blow-up in finite time in both cases with low initial energy and critical initial energy.
    Mathematics Subject Classification: Primary: 35B40, 35B44; Secondary: 35K20.

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