Numerical Mountain Pass and its Applications |
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| Authors: | Jiří Horák Gabriel J. Lord Mark A. Peletier |
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| Affiliation: | 1. Universität zu Köln, Germany;2. Heriot-Watt University, Edinburgh, United Kingdom;3. Technische Universiteit Eindhoven, The Netherlands |
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| Abstract: | The mountain pass theorem is an important tool in the calculus of variations and in finding solutions to nonlinear PDEs in general. The mountain pass structure can be exploited numerically, as well. We explain the main ideas on an example of buckling of a cylindrical shell. First, we prove existence of an MP-solution for almost all values of a given load parameter. Then, we find a numerical approximation of such a solution. Finally, we compare the results of a numerical continuation in the load parameter with results of physical experiments and make a few comments about further numerical investigations of the problem. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) |
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