Existence Results on Semi-Infinite Intervals for Nonlocal Evolutions Equations and Inclusions via Semigroup Theory

In this paper, we prove existence and controllability results on semi-infinite intervals for first- and second-order evolutions equations and inclusions in Banach spaces with nonlocal conditions. Our theory makes use of semigroups, cosine families, nonlinear alternative of Leray–Schauder, and a diagonalization argument.     

Existence of Solutions for Impulsive Neutral Integro-Differential Inclusions with Nonlocal Initial Conditions via Fractional Operators

This paper is mainly concerned with existence of mild solutions for first-order impulsive neutral integro-differential inclusions with nonlocal initial conditions in α-norm. We assume that the undelayed part generates an analytic resolvent operator and transforms it into an integral equation. By using a fixed point theorem for condensing multivalued maps, a main existence theorem is established. As an application of this main theorem, a practical consequence is derived for the sublinear growth case. Finally, we present an application to a neutral partial integro-differential equation with Dirichlet and nonlocal initial conditions.     

Quasilinear elliptic inclusions of Clarke's gradient type under local growth conditions

We consider a class of elliptic inclusions under Dirichlet boundary conditions involving multifunctions of Clarke's generalized gradient that satisfies only a one-sided local growth condition. An appropriate modification of the associated potential function along with truncation techniques will allow us to apply the theory of multivalued pseudomonotone operators for obtaining existence and comparison results under only one-sided local growth conditions on Clarke's generalized gradient.     

Boundary controllability of non-linear stochastic differential inclusions

The article is concerned with the boundary controllability of non-linear stochastic differential inclusions in a Banach space. Sufficient conditions for the boundary controllability are obtained by using a fixed point theorem for condensing maps due to Leray–Schauder non-linear alternative.     

Multidomain mixed variational analysis of transport flow through elastoviscoplastic porous media

Multidomain mixed nonlinear transport and flow phenomena through elastoviscoplastic porous media is variationally analyzed. Mixed variational formulations of the poro-mechanical system are established via composition duality methods, determining solvability results on the basis of duality principles. The conformation of the coupled physical system corresponds to constrained transport processes driven by a compressible Darcian flow, in a quasistatic elastoviscoplastic deformable subsurface porous media, modeled variationally by primal evolution mixed transport and consolidation, and dual evolution mixed flow and quasistatic deformation. For parallel computing, non-overlapping multidomain decomposition methods based on variational macro-hybridization, are presented and discussed, providing a natural multi-physics approach for the coupled transport flow and deformation system. For computational realizations, internal variational macro-hybrid mixed semi-discrete approximations are given, as well as primal and dual fully discrete semi-implicit time marching schemes. Furthermore, the corresponding coupled transport-flow-deformation system is concluded and analyzed, proposing natural resolution coupling techniques.     

A Proof of the Relaxation Theorem for Differential Inclusions Based on Euler Approximations

In this note, an alternative proof of the relaxation theorem is presented that is based on a two-level Euler approximation.     

Relaxation of Optimal Control Problems Involving Time Dependent Subdifferential Operators

This article provides in the setting of infinite dimensional Hilbert space, a result concerning the existence and uniqueness of solutions for Lipschitz single-valued perturbations of evolution problems associated with time-dependent subdifferential operators. The result is used to extend to optimal control problems associated with such equations the relaxation theorems with Young measures established in Casting et al. [7 C. Castaing , P. Raynaud de Fitte , and M. Valadier , M. ( 2004 ). Young Measures on Topological Spaces with Applications in Control Theory and Probability Theory . Kluwer Academic Publishers , Dordrecht . [Google Scholar], 11 J. F. Edmond and L. Thibault ( 2005 ). Relaxation of an optimal control problem involving a perturbed sweeping process . Math. Program Ser. B 104 : 347 – 373 .[Crossref], [Web of Science ®] , [Google Scholar]] and Edmond and Thibault [11 J. F. Edmond and L. Thibault ( 2005 ). Relaxation of an optimal control problem involving a perturbed sweeping process . Math. Program Ser. B 104 : 347 – 373 .[Crossref], [Web of Science ®] , [Google Scholar]].     

Melting of embedded anisotropic particles: PbIn inclusions in Al

Small particles embedded in the solid state can assume facetted shapes that indicate the anisotropy in interfacial free energy between the particle and the embedding phase. Previous in situ transmission electron microscopy (TEM) of Al–In has shown that such facetted nanoparticles with cubic symmetry embedded in a solid can produce a series of complex melt configurations. To determine the dependence of melt configuration on solid–solid facet energies, this work numerically calculates the equilibrium melt trajectory for a family of cuboctahedral particles parameterized by the ratio of matrix–particle interfacial free energies for orientations taken with respect to the crystal axes of the matrix, ??=?γ₁₀₀/γ₁₁₁. The calculations assume that equilibrium occurs with the minimization of the total interfacial free energy to determine the stable internal melt configuration for a fixed volume of melt confined within a member of the cuboctahedral family. At particular melt volume fractions, abrupt transitions in shape occur when a stable configuration reaches a touching or necking instability. In situ TEM of a dilute Al alloy containing embedded nanosized PbIn inclusions that gradually melt as the temperature is increased from 230 to 260°C is consistent with the results calculated for ??=?1.245.