$H^2$ convergence of solutions of a biharmonic problem on a truncated convex sector near the angle $\pi$
| Autor: | Abdelkader Tami, Mounir Tlemcani |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Applications of Mathematics. 66:383-395 |
| DOI: | 10.21136/am.2021.0284-19 |
| Popis: | We consider a biharmonic problem Δ2uω = fω with Navier type boundary conditions uω = Δuω = 0, on a family of truncated sectors Ωω in ℝ2 of radius r, 0 < r < 1 and opening angle ω, ω ∈ (2π/3, π] when ω is close to π. The family of right-hand sides (fω)ω∈(2π/3, π] is assumed to depend smoothly on ω in L2(Ωω). The main result is that uω converges to uπ when ω → π with respect to the H2-norm. We can also show that the H2-topology is optimal for such a convergence result. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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