On the stability of Bresse and Timoshenko systems with hyperbolic heat conduction

We investigate the stability of three thermoelastic beam systems with hyperbolic heat conduction. First, we study the Bresse-Gurtin-Pipkin system, providing a necessary and sufficient condition for the exponential stability and the optimal polynomial decay rate when the condition is violated. Second, we obtain analogous results for the Bresse-Maxwell-Cattaneo system, completing an analysis recently initiated in the literature. Finally, we consider the Timoshenko-Gurtin-Pipkin system and we find the optimal polynomial decay rate when the known exponential stability condition does not hold. As a byproduct, we fully recover the stability characterization of the Timoshenko-Maxwell-Cattaneo system. The classical "equal wave speeds" conditions are also recovered through singular limit procedures. Our conditions are compatible with some physical constraints on the coefficients as the positivity of the Poisson's ratio of the material. The analysis faces several challenges connected with the thermal damping, whose resolution rests on recently developed mathematical tools such as quantitative Riemann-Lebesgue lemmas.Comment: Abstract shortened and few typos correcte

Longtime Dynamics of a Semilinear Lamé System

This paper is concerned with longtime dynamics of semilinear Lamé systems ∂2 t u − μ u − (λ + μ)∇divu + α∂tu + f (u) = b, defined in bounded domains ofR3 with Dirichlet boundary condition. Firstly,we establish the existence of finite dimensional global attractors subjected to a critical forcing f (u).Writing λ + μ as a positive parameter ε, we discuss some physical aspects of the limit case ε → 0. Then, we show the upper-semicontinuity of attractors with respect to the parameter when ε → 0. To our best knowledge, the analysis of attractors for dynamics of Lamé systems has not been studied before

Stability of Multi-dimensional Nonlinear Piezoelectric Beam with Viscoelastic Infinite Memory

The long time behavior of a kind of fully magnetic effected nonlinear piezoelectric beam with viscoelastic infinite memory is considered. The well-posedness of this nonlinear coupled PDEs system is showed by mean of the semigroup theories and Banach fixed point theorem. Based on frequency domain analysis, it is proved that the corresponding coupled linear system can be indirectly stabilized exponentially by only one viscoelastic infinite memory term, which is located on one equation of these strongly coupled PDEs. Then the exponential decay of the solution to the nonlinear coupled PDEs' system is established by the energy estimation method under certain condition

[Book of abstracts]

USPCAPESCNPqFAPESPICMC Summer Meeting on Differential Equations (2016 São Carlos

The Crisis of the 14th Century: Teleconnections between Environmental and Societal Change?

Pre-modern critical interactions of nature and society can best be studied during the so-called "Crisis of the 14th Century". While historiography has long ignored the environmental framing of historcial processes and scientists have over-emphasized nature's impact on the course of human history, this volume tries to describe the at times complex modes of the late-medieval relationship of man and nature. The idea of 'teleconnection', borrowed from the geosciences, describes the influence of atmospheric circulation patterns often over long distances. It seems that there were 'teleconnections' in society, too. So this volumes aims to examine man-environment interactions mainly in the 14th century from all over Europe and beyond. It integrates contributions from different disciplines on impact, perception and reaction of environmental change and natural extreme events on late Medieval societies. For humanists from all historical disciplines it offers an approach how to integrate written and even scientific evidence on environmental change in established and new fields of historical research. For scientists it demonstrates the contributions scholars from the humanities can provide for discussion on past environmental changes