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Multidimensional Thermoelasticity for Nonsimple Materials - Well-Posedness and Long-Time Behavior

Anikushyn, Andrii; Pokojovy, Michael

Abstract: An initial-boundary value problem for the multidimensional type III thermoelaticity for a nonsimple material with a center of symmetry is considered. In the linear case, the well-posedness with and without Kelvin-Voigt and/or frictional damping in the elastic part as well as the lack of exponential stability in the elastically undamped case is proved. Further, a frictional damping for the elastic component is shown to lead to the exponential stability. A Cattaneo-type hyperbolic relaxation for the thermal part is introduced and the well-posedness and uniform stability under a nonlinear frictional damping are obtained using a compactness-uniqueness-type argument. Additionally, a connection between the exponential stability and exact observability for unitary C0-groups is established.


Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2016
Sprache Englisch
Identifikator DOI(KIT): 10.5445/IR/1000054399
ISSN: 2365-662X
URN: urn:nbn:de:swb:90-543992
KITopen ID: 1000054399
Verlag KIT, Karlsruhe
Umfang 28 S.
Serie CRC 1173 ; 2016/11
Schlagworte thermoelasticity, nonsimple materials, semilinear systems, well-posedness, uniform stability, hyperbolic relaxation
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