On exponential stability for von Kármán equations in the presence of thermal effects

Timoshenko's beam equation as limit of a nonlinear one-dimensional von Kármán system

“…Similar problems arise in two space dimensions. For instance, one may consider the full nonlinear von Kármán equations or related models (see [2,4] and the references therein) and try to show that it remains`close' to the two-dimensional Timoshenko's model,…”

“…A widely accepted dynamical model describing large de®ections of thin plates is the von Kármán system of equations. There is a large literature on this model specially in the last ten years or so, when several authors considered problems of existence, uniqueness, asymptotic behaviour in time (when some damping e¬ect is considered) as well as some other important properties (see [2,4,7] and the references therein).…”

Exponential decay rates for a full von Karman thermoelastic system with nonlinear thermal coupling

“…[Exponential decay rates for the energy of linear thermoelastic plates with γ = 0 (analytic case) have been known for some time [see [24,41,42,37,39]]. Similar results have been extended to several scalar nonlinear plate equations accounting for thermal components [2,11]. The one-dimensional full von Karman system accounting for in plane accelerations, with γ > 0, has been treated recently in [9].…”

Exponential decay for a von Kármán equations of memory type with acoustic boundary conditions

“…The problem of the stability of the solutions to a von Kármán system with dissipative effects has been studied by several authors. For example, in , the authors studied the von Kármán equation in the presence of thermal effects. In , the authors considered the von Kármán system with frictional dissipations effective in the boundary.…”