Return to search

Semilinear elastic waves with different damping mechanisms

Elastic waves describe particles vibrating in materials holding the property of elasticity. Particularly, several kinds of resistance in elasticity lead to the models of elastic waves with different damping mechanisms. In the thesis, the influence from friction, structural damping, Kelvin-Voigt damping on the linear and semilinear elastic waves in two or three dimensions are studied.

Concerning the Cauchy problem for linear elastic waves, some qualitative properties of solutions including well-posedness, smoothing effect, propagation of singularities, energy estimates and diffusion phenomena, are derived by using WKB analysis associated with diagonalization procedures or the spectral theory.

By constructing suitable time-weighted Sobolev spaces and using Banach's fixed point theorem, global (in time) existence of small data solutions to the weakly coupled systems for semilinear elastic waves with different damping terms have been proved. The main tools to treat the nonlinear terms in Sobolev spaces are some fractional tools in Harmonic Analysis.

Finally, well-posedness and Lp-Lq estimates for elastic waves without any damping terms in three dimensions are analyzed by employing Riesz transform theory and stationary phase methods.

Identiferoai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:71468
Date14 July 2020
CreatorsChen, Wenhui
ContributorsReissig, Michael, Technische Universität Bergakademie Freiberg
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
LanguageEnglish
Detected LanguageEnglish
Typeinfo:eu-repo/semantics/publishedVersion, doc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text
Rightsinfo:eu-repo/semantics/openAccess

Page generated in 0.0022 seconds