Advanced Search

We investigate the asymptotic behaviour, as $\epsilon \to 0$, of a class of monotone nonlinear Neumann problems, with growth $p-1$ ($p\in ]1,+\infty [$), on a bounded multidomain ${\Omega }_{\epsilon }\subset {ℝ}^N$ $(N\ge 2)$. The multidomain ${\Omega }_{\epsilon }$ is composed of two domains. The first one is a plate which becomes asymptotically flat, with thickness $h_{\epsilon }$ in the $x_N$ direction, as $\epsilon \to 0$. The second one is a “forest” of cylinders distributed with $\epsilon$-periodicity in the first $N-1$ directions on the upper side of the plate. Each cylinder has a small cross section of size $\epsilon$ and fixed...

We investigate the asymptotic behaviour, as ε → 0, of a class of monotone nonlinear Neumann problems, with growth -1 ( ∈]1, +∞[), on a bounded multidomain ${\Omega }_{\epsilon }\subset {ℝ}^N$ ( ≥ 2). The multidomain Ω is composed of two domains. The first one is a plate which becomes asymptotically flat, with thickness h in the direction, as ε → 0. The second one is a “forest" of cylinders distributed with -periodicity in the first - 1 directions on the upper side of the plate. Each cylinder has ...

We study the asymptotic behaviour of the following nonlinear problem: $$\{\begin{array}{c}-\mathrm{div}\left(a\left(D{u}_h\right)\right)+{\left|u_h\right|}^{p-2}{u}_h=f\text{in}{\Omega }_h,a\left(D{u}_h\right)·\nu =0\text{on}\partial {\Omega }_h,\hfill \end{array}.$$ in a domain Ω _h of ${ℝ}^n$ whose boundary ∂Ω _h contains an oscillating part with respect to h when h tends to ∞. The oscillating boundary is defined by a set of cylinders with axis 0...