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Nonlinear integro-differential models for intense waves in media like biological tissues and geostructures with complex internal relaxation-type dynamics
Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
2014 (English)In: Acoustical Physics, ISSN 1063-7710, E-ISSN 1562-6865, Vol. 60, no 4, 398-404 p.Article in journal (Refereed) Published
Abstract [en]

The paper discusses a universal scheme for constructing nonlinear integro-differential models to describe intense waves in media with a complex internal relaxation-type dynamics. Examples of such media are presented. Various forms of kernels are described. Situations are shown in which the models can be simplified by reducing them to differential or differential-difference equations with partial derivatives. Integral relations for the linear momentum and energy transferred by the wave are obtained. Exact solutions are found. The mapping method is used to obtain approximate solutions and analyze them in the form of difference relations.

Place, publisher, year, edition, pages
Maik Nauka/Springer , 2014. Vol. 60, no 4, 398-404 p.
Keyword [en]
nonlinearity, integro-differential equations, relaxation, kernel, absorption, dispersion, exact solution, shock wave
National Category
Applied Mechanics
URN: urn:nbn:se:bth-6594DOI: 10.1134/S1063771014040162ISI: 000339380800005Local ID: diva2:834112
Available from: 2014-10-10 Created: 2014-10-10 Last updated: 2016-09-01Bibliographically approved

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Rudenko, Oleg
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