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Let Ω be a bounded connected open subset of R N with a Lipschitz continuous boundary and f:R→R a locally Lipschitz continuous function such that f(0)=0, f is strictly convex on (0,+∞) and f′d(0)<−λ1(Ω) where λ1(Ω) is the smallest eigenvalue of (−Δ) in H 1 0(Ω), and f(s)→+∞ as...
We study how the equations of the potential of a semiconductor device, as described by Markowich (1986) and Selberherr (1984), behave when the width and the permittivity of the oxide region go to zero. According to their ratio, the problems converge to different asymptotic limits. This provides...
In this paper we consider the equations of small (acoustic) vibrations of a viscous compressible barotropic fluid in a bounded smooth domain under different boundary conditions. The structure of the spectrum is investigated; the estimates of the norm of the resolvent operator of the forced...
In this paper we consider an ordinary differential equation with nonlinearity which becomes constant if the solution amplitude increases. We use a modification of the Kuzmak–Whitham method, solutions of boundary layer type and a model Painleve equation. We constructed a global asymptotic...
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