Computer-assisted Existence Proofs for One-dimensional Schrödinger-Poisson Systems
  • Metaadatok
Tartalom: https://cyber.bibl.u-szeged.hu/index.php/actcybern/article/view/4034
Archívum: Acta Cybernetica
Gyűjtemény: Uncertainty Modeling, Software, Verified Computing and Optimization
Cím:
Computer-assisted Existence Proofs for One-dimensional Schrödinger-Poisson Systems
Létrehozó:
Wunderlich, Jonathan
Plum, Michael
Kiadó:
University of Szeged, Institute of Informatics
Dátum:
2020-03-16
Téma:
computer-assisted proof
existence
enclosure
Schrödinger-Poisson system
Tartalmi leírás:
Motivated by the three-dimensional time-dependent Schrödinger-Poisson system we prove the existence of non-trivial solutions of the one-dimensional stationary Schrödinger-Poisson system using computer-assisted methods. Starting from a numerical approximate solution, we compute a bound for its defect, and a norm bound for the inverse of the linearization at the approximate solution. For the latter, eigenvalue bounds play a crucial role, especially for the eigenvalues "close to" zero. Therefor, we use the Rayleigh-Ritz method and a corollary of the Temple-Lehmann Theorem to get enclosures of the crucial eigenvalues of the linearization below the essential spectrum. With these data in hand, we can use a fixed-point argument to obtain the desired existence of a non-trivial solution "nearby" the approximate one. In addition to the pure existence result, the used methods also provide an enclosure of the exact solution.
Nyelv:
angol
Típus:
info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Formátum:
application/pdf
Azonosító:
10.14232/actacyb.24.3.2020.6
Forrás:
Acta Cybernetica; Vol 24 No 3 (2020): Special Issue of the 11th Summer Workshop on Interval Methods; 373-391
2676-993X
0324-721X
Kapcsolat: