16 citations · 71 across the 33 of their papers we have counts for
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math.AP2010
The Peierls-Nabarro model as a limit of a Frenkel-Kontorova model
Ahmad Fino, Hassan Ibrahim, Régis Monneau
We study a generalization of the fully overdamped Frenkel-Kontorova model in dimension This model describes the evolution of the position of each atom in a crystal, and…
math.AP2010★ 9 cited
Finite time blow-up for a wave equation with a nonlocal nonlinearity
Ahmad Fino, Mokhtar Kirane, Vladimir Georgiev
In this article, we study the local existence of solutions for a wave equation with a nonlocal in time nonlinearity. Moreover, a blow-up results are proved under some conditions on…
math.AP2010
Critical exponent for damped wave equations with nonlinear memory
Ahmad Fino
We consider the Cauchy problem in for a semilinear damped wave equation with nonlinear memory. Global existence and asymptotic behavior as $t\rightarrow\…