Nonlocal General Boundary Value Problems of Elliptic Type in <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript> Cases

This paper is devoted to the study of operational second-order differential equations of elliptic type with nonregular coefficient-operator boundary conditions. In the framework of UMD spaces, we give some new results by using semi-groups and interpolation theory. We define two types of solutions: semi-strict and strict solutions. We then characterizes the existence and uniqueness of such solutions.     

Homogenization of magneto-electro-elastic multilaminated materials

In this work, based on the periodic unfolding homogenizationtechnique, the limiting equations modelling the behaviour ofthree-dimensional magneto-electro-elastic periodic structuresare rigorously established. The local problems and the correspondinghomogenized coefficients of the elastic, dielectric, magneticpermittivity, piezoelectric, piezomagnetic and magneto-electric(ME) tensors are explicitly described. The homogenization modelis exemplified for laminated composites and a unified generalformula for all effective properties of periodic multilaminatedmagneto-electro-elastic composites is obtained. This formulais applied to investigate the global behaviour for the importantcase of transversely isotropic constituents and any finite numberof layers in each periodic cell. Examples that provide theoreticalevidence of the presence of both a product property and theME effect are given.     

Nonlinear damped Timoshenko systems with second sound—Global existence and exponential stability

In this paper, we consider nonlinear thermoelastic systems of Timoshenko type in a one‐dimensional bounded domain. The system has two dissipative mechanisms being present in the equation for transverse displacement and rotation angle—a frictional damping and a dissipation through hyperbolic heat conduction modelled by Cattaneo's law, respectively. The global existence of small, smooth solutions and the exponential stability in linear and nonlinear cases are established. Copyright © 2008 John Wiley & Sons, Ltd.     

Decay property of Timoshenko system in thermoelasticity

We investigate the decay property of a Timoshenko system of thermoelasticity in the whole space for both Fourier and Cattaneo laws of heat conduction. We point out that although the paradox of infinite propagation speed inherent in the Fourier law is removed by changing to the Cattaneo law, the latter always leads to a solution with the decay property of the regularity‐loss type. The main tool used to prove our results is the energy method in the Fourier space together with some integral estimates. We derive L² decay estimates of solutions and observe that for the Fourier law the decay structure of solutions is of the regularity‐loss type if the wave speeds of the first and the second equations in the system are different. For the Cattaneo law, decay property of the regularity‐loss type occurs no matter what the wave speeds are. In addition, by restricting the initial data to with a suitably large s and γ ∈ [0,1], we can derive faster decay estimates with the decay rate improvement by a factor of t^?γ/2. Copyright © 2011 John Wiley & Sons, Ltd.     

Comparison of two approaches for the discretization of elastodynamic contact problems

The purpose of this Note is to compare two approaches for the discretization of elastodynamic contact problems. First, we introduce an energy conserving method based on a standard midpoint scheme and a contact condition expressed in terms of velocity. The second approach consists in considering an equivalent distribution of the body mass so that the nodes on the contact boundary have no inertia. We prove that this method leads to an energy conservation for the space semi-discretized elastodynamic contact problem. Finally, some numerical results are presented in the two dimensional case. To cite this article: H.B. Khenous et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Exponential stability in one‐dimensional non‐linear thermoelasticity with second sound

In this paper, we consider a one‐dimensional non‐linear system of thermoelasticity with second sound. We establish an exponential decay result for solutions with small ‘enough’ initial data. This work extends the result of Racke (Math. Methods Appl. Sci. 2002; 25 :409–441) to a more general situation. Copyright © 2004 John Wiley & Sons, Ltd.     

Novel prodrugs for targeting diagnostic and therapeutic radionuclides to solid tumors

Most cancer therapeutics (chemo, radiation, antibody-based, anti-angiogenic) are at best partially and/or temporarily effective. In general, the causes for failure can be summarized as: (i) poor diffusion and/or nonuniform distribution of drug/prodrug molecules in solid tumors; (ii) high drug concentration and retention in normal tissues (leading to side effects); (iii) requirement for plasma-membrane permeability and/or internalization of drug/prodrug molecules; (iv) low uptake of drug by tumor; (v) lack of retention of drug within tumor (most have gradient-driven reversible binding); and (vi) multidrug resistance. We are developing an innovative technology that aims to surmount these problems by actively concentrating and permanently entrapping radioimaging and radiotherapeutic prodrugs specifically within solid tumors. The approach will enable noninvasive sensing (imaging) and effective therapy of solid tumors, allowing tumor detection, diagnosis, and treatment to be closely coupled (personalized medicine).