Homogenization results for the generator of multiscale Langevin dynamics in weighted Sobolev spaces
We study the homogenization of the Poisson equation with a reaction term and of the eigenvalue problem associated to the generator of multiscale Langevin dynamics. Our analysis extends the theory of two-scale convergence to the case of weighted Sobolev spaces in unbounded domains. We provide converg...
Saved in:
| Published in | IMA journal of applied mathematics Vol. 88; no. 1; pp. 67 - 101 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
01.04.2023
|
| Online Access | Get full text |
Cover
Loading…
| Summary: | We study the homogenization of the Poisson equation with a reaction term and of the eigenvalue problem associated to the generator of multiscale Langevin dynamics. Our analysis extends the theory of two-scale convergence to the case of weighted Sobolev spaces in unbounded domains. We provide convergence results for the solution of the multiscale problems above to their homogenized surrogate. A series of numerical examples corroborate our analysis. |
|---|---|
| ISSN: | 0272-4960 1464-3634 |
| DOI: | 10.1093/imamat/hxad003 |