We study a nonlocal wave equation with logarithmic damping, which is rather weak in the low-frequency zone as compared with frequently studied strong damping case. We consider the Cauchy problem for this model in Rn, and we study the asymptotic profile and optimal estimates of the solutions and the total energy as t → ∞ in L2 sense. In that case, some results on hypergeometric functions are useful.
Asymptotic profiles for a wave equation with parameter-dependent logarithmic damping
D'Abbicco M.;
2021-01-01
Abstract
We study a nonlocal wave equation with logarithmic damping, which is rather weak in the low-frequency zone as compared with frequently studied strong damping case. We consider the Cauchy problem for this model in Rn, and we study the asymptotic profile and optimal estimates of the solutions and the total energy as t → ∞ in L2 sense. In that case, some results on hypergeometric functions are useful.File in questo prodotto:
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