In this paper we prove a H-convergence type result for the homogenization of systems the coefficients of which satisfy a functional ellipticity condition and a strong equi-integrability condition. The equi-integrability assumption allows us to control the fact that the coefficients are not equi-bounded. Since the truncation principle used for scalar equations does not hold for vector-valued systems, we present an alternative approach based on an approximation result by Lipschitz functions due to...

The aim of this paper is to give a general idea to state optimality conditions of control problems in the following form: ${\displaystyle \underset{{\displaystyle (u,v)\in {𝒰}_{ad}}}{inf}{\int }_0^{1}f\left(t,u\left({\theta }_v\left(t\right)\right),u^{\text{'}}\left(t\right),v\left(t\right)\right)\mathrm{d}t}$, (1) where ${𝒰}_{ad}$ is a set of admissible controls and ${\theta }_v$ is the solution of the following equation: $\{\frac{\mathrm{d}\theta \left(t\right)}{\mathrm{d}t}=g(t,\theta \left(t\right),v\left(t\right)),t\in [0,1]$ ; ${\displaystyle \theta \left(0\right)={\theta }_0,\theta \left(t\right)\in [0,1]\forall t}$. (2). The results are nonlocal and new.

The paper deals with the analysis and the numerical solution of the topology optimization of system governed by variational inequalities using the combined level set and phase field rather than the standard level set approach. The standard level set method allows to evolve a given sharp interface but is not able to generate holes unless the topological derivative is used. The phase field method indicates the position of the interface in a blurry way but is flexible in the holes generation. In the...

Scalar parameter values as well as initial condition values are to be identified in initial value problems for ordinary differential equations (ODE). To achieve this goal, computer algebra tools are combined with numerical tools in the MATLAB environment. The best fit is obtained through the minimization of the summed squares of the difference between measured data and ODE solution. The minimization is based on a gradient algorithm where the gradient of the summed squares is calculated either numerically...

We consider a class of second-gradient elasticity models for which the internal potential energy is taken as the sum of a convex function of the second gradient of the deformation and a general function of the gradient. However, in consonance with classical nonlinear elasticity, the latter is assumed to grow unboundedly as the determinant of the gradient approaches zero. While the existence of a minimizer is routine, the existence of weak solutions is not, and we focus our efforts on that question...

We consider a class of second-gradient elasticity models for which the internal potential energy is taken as the sum of a convex function of the second gradient of the deformation and a general function of the gradient. However, in consonance with classical nonlinear elasticity, the latter is assumed to grow unboundedly as the determinant of the gradient approaches zero. While the existence of a minimizer is routine, the existence of weak solutions is not, and we focus our efforts on that question...

This paper studies the attainable set at time T>0 for the control system $$\dot{y}\left(t\right)=f(y\left(t\right),u\left(t\right))u\left(t\right)\in U$$ showing that, under suitable assumptions on f, such a set satisfies a uniform interior sphere condition. The interior sphere property is then applied to recover a semiconcavity result for the value function of time optimal control problems with a general target, and to deduce C1,1-regularity for boundaries of attainable sets.

This paper presents the role of vector relative degree in the formulation of stationarity conditions of optimal control problems for affine control systems. After translating the dynamics into a normal form, we study the Hamiltonian structure. Stationarity conditions are rewritten with a limited number of variables. The approach is demonstrated on two and three inputs systems, then, we prove a formal result in the general case. A mechanical system example serves as illustration.