Timoshenko systems with fading memory

The decay properties of the semigroup generated by a linear Timoshenko system with fading memory are discussed. Uniform stability is shown to occur within a necessary and sufficient condition on the memory kernel

Stability analysis of abstract systems of Timoshenko type

We consider an abstract system of Timoshenko type $$\begin{cases} \rho_1{{\ddot \varphi}} + a A^{\frac12}(A^{\frac12}\varphi + \psi) =0\\ \rho_2{{\ddot \psi}} + b A \psi + a (A^{\frac12}\varphi + \psi) - \delta A^\gamma {\theta} = 0\\ \rho_3{{\dot \theta}} + c A\theta + \delta A^\gamma {{\dot \psi}} =0 \end{cases}$$ where the operator $A$ is strictly positive selfadjoint. For any fixed $\gamma\in\mathbb{R}$, the stability properties of the related solution semigroup $S(t)$ are discussed. In particular, a general technique is introduced in order to prove the lack of exponential decay of $S(t)$ when the spectrum of the leading operator $A$ is not made by eigenvalues only.Comment: Corrected typo

Testing creation of matter with neutrinoless double beta decay

In this brief review, the importance of the so called neutrinoless double beta decay transition in the search for physics beyond the Standard Model is emphasized. The expectations for the transition rate are examined in the assumption that ordinary neutrinos have Majorana masses. We stress the relevance of cosmological measurements and discuss the uncertainties implied by nuclear physics.Comment: 9 pages. Based on the review paper Neutrinoless double beta decay: 2015 review, Adv.High Energy Phys. 2016 (2016) 2162659. To appear in the proceedings of the XVII International Workshop on Neutrino Telescopes 13-17 March 2017, Venice, Ital

A quantitative Riemann-Lebesgue lemma with application to equations with memory

An elementary proof of a quantitative version of the Riemann-Lebesgue lemma for functions supported on the half line is given. Applications to differential models with memory are discussed

Steady states of elastically-coupled extensible double-beam systems

Given $\beta\in\mathbb{R}$ and $\varrho,k>0$, we analyze an abstract version of the nonlinear stationary model in dimensionless form $$\begin{cases} u"" - \Big(\beta+ \varrho\int_0^1 |u'(s)|^2\,{\rm d} s\Big)u" +k(u-v) = 0 v"" - \Big(\beta+ \varrho\int_0^1 |v'(s)|^2\,{\rm d} s\Big)v" -k(u-v) = 0 \end{cases}$$ describing the equilibria of an elastically-coupled extensible double-beam system subject to evenly compressive axial loads. Necessary and sufficient conditions in order to have nontrivial solutions are established, and their explicit closed-form expressions are found. In particular, the solutions are shown to exhibit at most three nonvanishing Fourier modes. In spite of the symmetry of the system, nonsymmetric solutions appear, as well as solutions for which the elastic energy fails to be evenly distributed. Such a feature turns out to be of some relevance in the analysis of the longterm dynamics, for it may lead up to nonsymmetric energy exchanges between the two beams, mimicking the transition from vertical to torsional oscillations

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