When solving boundary value problems on infinite intervals, it is possible to use continuation principles. Some of these principles take advantage of equipping the considered function spaces with topologies of uniform convergence on compact subintervals. This makes the representing solution operators compact (or condensing), but, on the other hand, spaces equipped with such topologies becomemor...

We consider a scalar elliptic equation for a composite medium consisting of homogeneous C1,α0 inclusions, 0 < α0 ≤ 1, embedded in a constant matrix phase. When the inclusions are separated and are separated from the boundary, the solution has an integral representation, in terms of potential functions defined on the boundary of each inclusion. We study the system of integral equations satisfied...

We study the existence of solutions for fractional integrodifferential inclusions of order q ∈ (1, 2] with families of mixed, closed, strip and integral boundary conditions. We establish Filippov type existence results in the case of nonconvex set-valued maps.

In physics, engineering and other settings, it is important to understand the macroscopic behaviour of systems whose evolution is determined by microscale effects. It seems natural to consider these microscale effects to be random in nature (and, therefore, beyond the scope of classical averaging and homogenization theory) and to constitute some perturbation of a well-understood smooth structur...

The existence results for an abstract Cauchy problem involving a higher order differential inclusion with infinite delay in a Banach space are obtained. We use the concept of the existence family to express the mild solutions and impose the suitable conditions on the nonlinearity via the measure of noncompactness in order to apply the theory of condensing multimaps for the demonstration of our ...

Impulse differential inclusions, and in particular, hybrid control systems, are defined by a differential inclusion (or a control system) and a reset map. A run of an impulse differential inclusion is defined by a sequence of cadences, of reinitialized states and of motives describing the evolution along a given cadence between two distinct consecutive impulse times, the value of a motive at th...

We study the existence theory to quasistatic initial-boundary value problems with internal variables, which model the viscoelastic or viscoplastic behavior of solids at small strain. In these problems a system of linear partial differential equations coupled with a nonlinear system of differential equations or differential inclusions must be solved. The solution theory is based on monotonicity ...

The paper introduces model ensembles as a common framework for understanding qualitative differential equations (QDEs) and differential inclusions in a precise mathematical sense. It provides basic insights into the communalities and differences of both approaches to model under uncertainty. On this basis, a set of established methods for QDEs, some hybrid methods and standard quantitative meth...

We derive an effective medium theory that predicts the bulk and shear moduli of composite materials consisting of a matrix material with soft or hard ellipsoidal inclusions. The theory predicts that diskshaped inclusions are most effective for softening or hardening a composite material. The theory is applied to the design of materials with highly absorptive acoustical properties. DTIC TAB0 UJn...

Let F = F(t, x) be a bounded, Hausdorff continuous multifunction with compact, totally disconnected values. Given any y0 ∈ F(t0, x0), we show that the differential inclusion ẋ ∈ F(t, x)⊂ Rm has a globally defined classical solution, with x(t0)= x0, ẋ(t0)= y0. © 2008 Elsevier Inc. All rights reserved.