Long-time behavior of quasilinear thermoelastic Kirchhoff–Love plates with second sound. (September 2019)

• Record Type: Journal Article
• Authors: Lasiecka, Irena; Pokojovy, Michael; Wan, Xiang
• Is Part Of: Nonlinear analysis. Volume 186(2019)
• Page Start: 219
• Page End: 258
• Publication Date: 2019-09
• Subjects: primary 35L57 35Q74 74B20 74F05 74K20 -- secondary 35A01 35A02 35A09 35B40 35B65; Kirchhoff–Love plates -- Nonlinear thermoelasticity -- Hyperbolic thermoelasticity -- Global well-posedness -- Classical solutions -- Exponential stability; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.02.019
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider an initial–boundary-value problem for a thermoelastic Kirchhoff & Love plate, thermally insulated and simply supported on the boundary, incorporating rotational inertia and a quasilinear hypoelastic response, while the heat effects are modeled using the hyperbolic Maxwell–Cattaneo–Vernotte law giving rise to a 'second sound' effect. We study the local well-posedness of the resulting quasilinear mixed-order hyperbolic system in a suitable solution class of smooth functions mapping into Sobolev H k -spaces. Exploiting the sole source of energy dissipation entering the system through the hyperbolic heat flux moment, provided the initial data are small – not in the full topology of our solution class, but in a lower topology corresponding to weak solutions we prove a nonlinear stabilizability estimate furnishing global existence & uniqueness and exponential decay of classical solutions.