Mathematics – Analysis of PDEs
Scientific paper
2009-02-04
Mathematics
Analysis of PDEs
Scientific paper
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 $\Omega_1$ of the domain of integration of $\Omega$. We generalize Lions' results to covering the case of diffusivities which are piecewise $C^1$ up to the boundary of $\Omega_1$ and $\Omega_2$, where $\Omega_2 := \Omega \setminus \overline{\Omega}_1$ instead of piecewise constant coefficients. In addition, we extend both Lions' and our previous results by providing the strong convergence of $(A_{\bar{p}_\nu}^{-1})_{\nu \in \mathbb{N}^\ast},$ for a monotonically decreasing sequence of diffusivities $(\bar{p}_\nu )_{\nu \in \mathbb{N}^\ast}$.
Aksoylu Burak
Beyer Horst R.
No associations
LandOfFree
On the characterization of asymptotic cases of the diffusion equation with rough coefficients and applications to preconditioning does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the characterization of asymptotic cases of the diffusion equation with rough coefficients and applications to preconditioning, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the characterization of asymptotic cases of the diffusion equation with rough coefficients and applications to preconditioning will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-25153