A method for obtaining approximate solutions for highly dynamic problems
| dc.contributor.author | Kotooussov, A. | |
| dc.date.issued | 2001 | |
| dc.description | Copyright © 2001 Elsevier Science Ltd. All rights reserved. | |
| dc.description.abstract | As a rule, a theoretical analysis of the behavior of highly dynamic systems is very difficult due to the strong non-linearity of the governing equations. Basic results are usually achieved by the application of the inverse scattering transform methods, methods of perturbation theory and numerical approaches. However, all the above-mentioned methods and approaches have well-known limits in their application. In this paper, a dynamic system described by linear hyperbolic partial differential equations with a non-linearity localized in a space-time domain is considered. The application of the theory of laws of conservation together with the Huygens' principle allows the generation of a family of integral inequalities by using the solution of the corresponding linear problem with the same initial data. In turn, these integral inequalities make it possible to formally reduce the initial problem for locally non-linear hyperbolic equations to an extremal problem at limitations (restrictions) defined by these integral inequalities. Thus, upper and lower bound estimates of the solution of the locally non-linear problem can be obtained from the solution of this extremal problem to which standard techniques can be applied. The method under development has many advantages when compared with known approaches. These advantages together with its limitations are discussed in this paper. Examples of this new method as applied to some locally non-linear problems of dynamic elasticity are also considered. | |
| dc.description.statementofresponsibility | A. G. Kotousov | |
| dc.description.uri | http://www.elsevier.com/wps/find/journaldescription.cws_home/278/description#description | |
| dc.identifier.citation | International Journal of Engineering Science, 2001; 39(4):477-489 | |
| dc.identifier.doi | 10.1016/S0020-7225(00)00046-X | |
| dc.identifier.issn | 0020-7225 | |
| dc.identifier.orcid | Kotooussov, A. [0000-0001-9337-5095] | |
| dc.identifier.uri | http://hdl.handle.net/2440/40230 | |
| dc.language.iso | en | |
| dc.publisher | Pergamon-Elsevier Science Ltd | |
| dc.source.uri | https://doi.org/10.1016/s0020-7225(00)00046-x | |
| dc.title | A method for obtaining approximate solutions for highly dynamic problems | |
| dc.type | Journal article | |
| pubs.publication-status | Published |