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A competition on blow-up for semilinear wave equations with scale-invariant damping and nonlinear memory term

  • *Corresponding author: Ahmad Z. Fino

    *Corresponding author: Ahmad Z. Fino
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  • In this paper, we investigate blow-up of solutions to semilinear wave equations with scale-invariant damping and nonlinear memory term in $ \mathbb{R}^n $, which can be represented by the Riemann-Liouville fractional integral of order $ 1-\gamma $ with $ \gamma\in(0, 1) $. Our main interest is to study mixed influence from damping term and the memory kernel on blow-up conditions for the power of nonlinearity, by using test function method or generalized Kato's type lemma. We find a new competition, particularly for the small value of $ \gamma $, on the blow-up range between the effective case and the non-effective case.

    Mathematics Subject Classification: 35B44, 35L05, 35L71, 26A33, 35B33.

    Citation:

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