Asymptotic Analysis

This paper proves that any initial condition in the energy space for the system of thermoelastic plates without rotatory inertia on a smooth bounded domain with hinged mechanical boundary conditions and Dirichlet thermal boundary condition can be steered to zero by a square integrable input function, either mechanical or thermal, supported in arbitrarily small sub-domain and time interval [0,T]. As T tends to zero, for initial states with unit energy norm, the norm of this input function grows at most like exp (C_p/T^p) for any real p>1 and some C_p>0. These results are analogous to the optimal ones known for the heat flow and the proof uses the heat control strategy of Lebeau and Robbiano.

This paper is concerned with a fourth-order degenerate parabolic equation, namely the thin film equation, in one space dimension which describes the dewetting phenomenon of a thin film under the long-range attractive force and the short-range stabilizing effect of Born repulsion. The existence of global attractor is proved.

A method of formal scaling is presented that allows for a unified deduction from three-dimensional linear elasticity of the equations of structural mechanics, such as Reissner–Mindlin's equations for shearable plates and Timoshenko's equations for shearable rods. This method is based on the requirement that a scaled energy functional that may include second-gradient terms stay bounded in the limit of vanishing thickness.

This paper considers heat equations with local and coupled localized sources subject to null Dirichlet boundary conditions. The behavior of solutions depends on the interactions among the local and localized sources as well as the diffusions with the null boundary conditions in the model. The aim of the paper is to distinguish total and single point blow-up for the non-global solutions. In addition, simultaneous versus non-simultaneous blow-up of solutions under different dominations are determined also with four possible simultaneous blow-up rates.

In this paper, we investigate the homogenization of a nonlinear kinetic equation modeling electron transport in semiconductors. We compute effective scattering coefficients for medium with periodic inhomogeneities.

In this paper, the scattering theory for the Schrödinger–improved Boussinesq system in two space dimensions is studied. The local Cauchy problem at infinite initial time of this system for given final data is considered, and the existence of a unique asymptotically free solution to this system is proved when the Schrödinger data is suitably small.