Lyapunov functionals for reaction–diffusion equations with memory

We consider a reaction‐diffusion equation in which the usual diffusion term also depends on the past history of the diffusion itself. This equation has been analysed by several authors, with an emphasis on the longtime behaviour of the solutions. In this respect, the first results have been obtained by using the past history approach. They show that the equation, subject to a suitable boundary condition, defines a dissipative dynamical system which possesses a global attractor. A similar theorem has been recently proved by Chepyzhov and Miranville, using a different method based on the notion of trajectory attractors. In addition, those authors provide sufficient conditions that ensure the existence of a Lyapunov functional. Here we show that a similar result can be demonstrated within the past history approach, with less restrictive conditions. Copyright © 2005 John Wiley & Sons, Ltd.     

Nonclassical diffusion with memory

We consider the nonclassical diffusion equation with hereditary memory on a bounded three‐dimensional domain. Setting the problem in the past history framework, and with very general assumptions on the memory kernel κ, we prove that the related solution semigroup possesses a global attractor of optimal regularity. Copyright © 2014 John Wiley & Sons, Ltd.     

A Gronwall-type lemma with parameter and dissipative estimates for PDEs

We discuss the problem of establishing dissipative estimates for certain differential equations for which the usual methods apparently do not work. The main tool is a new Gronwall-type lemma with parameter. As an application, we consider a semilinear equation of viscoelasticity with low dissipation.     

Improved measurement of the K+-->pi+nunu; branching ratio

An additional event near the upper kinematic limit for K+-->pi(+)nunu; has been observed by experiment E949 at Brookhaven National Laboratory. Combining previously reported and new data, the branching ratio is B(K+-->pi(+)nunu;)=(1.47(+1.30)(-0.89))x10(-10) based on three events observed in the pion momentum region 211相似文献   

Periodic solutions of asymptotically linear second order equations with indefinite weight

In this paper we study the ordinary differential equation

On Partial Compositeness and the CP asymmetry in charm decays

Recently, the LHCb and CDF Collaborations reported the measure of an unexpectedly large direct CP asymmetry in D meson decays. In this paper we ask if new physics associated with Partial Compositeness could plausibly explain this result. We find that Composite Higgs models with mass scale around 10 TeV can account for it, while marginally satisfying all other flavor constraints in the quark sector. The minimal framework is however inadequate in the lepton sector due to the strong constraint from μ→eγ$\mu \to e\gamma$. This tension can be efficiently alleviated by realizing Partial Compositeness within Supersymmetry. The resulting models can saturate the CP asymmetry in D decays for superpartner masses close to the TeV scale and somewhat large A-terms. The supersymmetric realization of Partial Compositeness also offers a predictive and phenomenologically viable organizing principle for R-parity violation, and may result in very distinctive signatures at hadron colliders. With or without Supersymmetry, the neutron EDM is expected to be around the present experimental sensitivity.     

Stability analysis of abstract systems of Timoshenko type

We consider an abstract system of Timoshenko type

$$\begin{aligned} \left\{ {\begin{array}{l} \rho_1{{\ddot \varphi}} + a A^{\frac12}(A^{\frac12}\varphi + \psi) =0\\\rho_2{{\ddot \psi}} + b A \psi + a (A^{\frac12}\varphi + \psi) -\delta A^\gamma {\theta} = 0\\\rho_3{{\dot \theta}} + c A\theta + \delta A^\gamma {{\dot \psi}} =0 \end{array}} \right. \end{aligned}$$

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 \({A}\) does not consist of eigenvalues only.