On the characterization of asymptotic cases of the diffusion equation with rough coefficients and applications to preconditioning
| dc.creator | Aksoylu, Burak | |
| dc.creator | Beyer, Horst R. | |
| dc.date | 2009-02-04 | |
| dc.date.accessioned | 2026-07-07T12:37:38Z | |
| dc.date.available | 2026-07-07T12:37:38Z | |
| dc.description | We consider the diffusion equation in the setting of operator theory. In particular, we study the characterization of the limit of the diffusion operator for diffusivities approaching zero on a subdomain $Ω_1$ of the domain of integration of $Ω$. We generalize Lions' results to covering the case of diffusivities which are piecewise $C^1$ up to the boundary of $Ω_1$ and $Ω_2$, where $Ω_2 := Ω\setminus \overlineΩ_1$ instead of piecewise constant coefficients. In addition, we extend both Lions' and our previous results by providing the strong convergence of $(A_{\bar{p}_ν}^{-1})_{ν\in \mathbb{N}^\ast},$ for a monotonically decreasing sequence of diffusivities $(\bar{p}_ν)_{ν\in \mathbb{N}^\ast}$. | |
| dc.identifier | https://arxiv.org/abs/0902.0788 | |
| dc.identifier | http://arxiv.org/abs/0902.0788 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/218505 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Functional Analysis | |
| dc.subject | 35J25, 47F05, 65J10, 65N99 | |
| dc.title | On the characterization of asymptotic cases of the diffusion equation with rough coefficients and applications to preconditioning | |
| dc.type | text |