Computer-assisted enclosures for fourth order elliptic equations
Abstract:
We describe a computer-assisted method for proving existence and multiplicity of solutions of fourth order nonlinear elliptic boundary value problems: we compute a good
numerical approximation of a solution and certain defect bounds with computer-assistance, and then obtain a rigorous proof of the existence of an exact solution close to the numerical one by a fixed-point argument.
numerical approximation of a solution and certain defect bounds with computer-assistance, and then obtain a rigorous proof of the existence of an exact solution close to the numerical one by a fixed-point argument.
| Zugehörige Institution(en) am KIT | Institut für Analysis (IANA) |
| Publikationstyp | Hochschulschrift |
| Publikationsjahr | 2012 |
| Sprache | Englisch |
| Identifikator | urn:nbn:de:swb:90-292809 KITopen-ID: 1000029280 |
| Verlag | Karlsruher Institut für Technologie (KIT) |
| Art der Arbeit | Dissertation |
| Fakultät | Fakultät für Mathematik (MATH) |
| Institut | Institut für Analysis (IANA) |
| Prüfungsdaten | 11.07.2012 |
| Schlagwörter | Fourth order semilinear elliptic boundary value problems, computer-assisted proofs |
| Referent/Betreuer | Plum, M. |