## Displaying similar documents to “Homogenization of highly oscillating boundaries and reduction of dimension for a monotone problem”

### Asymptotic behavior of second-order dissipative evolution equations combining potential with non-potential effects

ESAIM: Control, Optimisation and Calculus of Variations

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In the setting of a real Hilbert space $ℋ$, we investigate the asymptotic behavior, as time t goes to infinity, of trajectories of second-order evolution equations            ü(t) + γ $\stackrel{˙}{u}$(t) + ϕ(u(t)) +

### Asymptotic behavior of the hitting time, overshoot and undershoot for some Lévy processes

ESAIM: Probability and Statistics

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Let () be a Lévy process started at , with Lévy measure . We consider the first passage time of () to level , and the overshoot and the undershoot. We first prove that the Laplace transform of the random triple () satisfies some kind of integral equation. Second, assuming that admits exponential moments, we show that $\left(\stackrel{˜}{{T}_{x}},{K}_{x},{L}_{x}\right)$ converges in distribution as → ∞, where $\stackrel{˜}{{T}_{x}}$ denotes a suitable renormalization of .

### Non-Trapping sets and Huygens Principle

ESAIM: Mathematical Modelling and Numerical Analysis

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We consider the evolution of a set $\Lambda \subset {ℝ}^{2}$ according to the Huygens principle: the domain at time , Λ, is the set of the points whose distance from is lower than . We give some general results for this evolution, with particular care given to the behavior of the perimeter of the evoluted set as a function of time. We define a class of sets (non-trapping sets) for which the perimeter is a continuous function of , and we give an algorithm to approximate the evolution. Finally we restrict...

### Towards parametrizing word equations

RAIRO - Theoretical Informatics and Applications

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Classically, in order to resolve an equation ≈ over a free monoid *, we reduce it by a suitable family $ℱ$ of substitutions to a family of equations ≈ , $f\in ℱ$, each involving less variables than ≈ , and then combine solutions of ≈ into solutions of ≈ . The problem is to get $ℱ$ in a handy form. The method we propose consists in parametrizing the path traces in the so called associated to ≈ . We carry out such a parametrization in the case the prime equations in the graph involve at...