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Abstract

In this work we study decay rates for a σ-evolution equation in $R^{n}$ under effects of a damping term represented by the action of a fractional Laplacian operator and a time-dependent coefficient, $b (t) {(- Δ)}^{θ} u_{t} (t, x)$ . We consider that b is ‘confined’ in the curve $g (t) = {(1 + t)}^{α} {ln}^{γ} (1 + t)$ for large $t ⩾ t_{0}$ and without any control on $\frac{d}{d t} b (t)$ .

Keywords

Wave equation plate equation fractional damping sharp decay rates non-effective damping multiplier method

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σ -Evolution models with low regular time-dependent non-effective structural damping

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