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"Concerning (partial) differential equations, amongst many others two questions are of great importance: existence and uniqueness, or more general multiplicity of solutions... There are plenty of equations, where analytical methods fail to work." The author describes in this work a computer-assisted method for proving existence and multiplicity of solutions of fourth order nonlinear elliptic boundary value problems. The main idea of this method is to compute a good numerical approximation of a solution and certain defect bounds with computer-assistance. Then a rigorous proof of the existence of an exact solution close to the numerical one is obtained by a fixed-point argument. The efficiency of this method is demonstrated with the examples of the fourth order Gelfand- and Emden-equations on various domains.
| Autorius: | Borbála Fazekas |
| Leidėjas: | Südwestdeutscher Verlag für Hochschulschriften AG Co. KG |
| Išleidimo metai: | 2015 |
| Knygos puslapių skaičius: | 152 |
| ISBN-10: | 3838118340 |
| ISBN-13: | 9783838118345 |
| Formatas: | 220 x 150 x 10 mm. Knyga minkštu viršeliu |
| Kalba: | Anglų |
Parašykite atsiliepimą apie „Computer-assisted enclosures for fourth order elliptic equations: Multiplicity of solutions of nonlinear equations“
