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Computer-assisted enclosures for fourth order elliptic equations

Name: Computer-assisted enclosures for fourth order elliptic equations
Brand: Sudwestdeutscher Verlag Fur Hochschulschriften AG
SKU: 06936262
Price: 61.49 EUR
Availability: InStock
Author: Borbála Fazekas
ISBN: 9783838118345

Borbála Fazekas

Language

English

Book Paperback

Libristo code: 06936262

Publishers Sudwestdeutscher Verlag Fur Hochschulschriften AG, September 2012

"Concerning (partial) differential equations, amongst many others two questions are of great importa... Full description

Libristo code: 06936262

150 b

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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.