We discuss existence, uniqueness, and homogenization results for a class of rate-independent, nonlinear ferroelectric models. We show that these models can be formulated in an energetic framework which is based on the elastic and the electric displacements as reversible variables and on interior, irreversible variables like the remanent polarization. The PDE system defining the model is restate...

Risk-sensitive criteria have been used to derive robust filters, identifiers, and controllers. The fundamental issues of existence and uniqueness of an estimate of a random variable given a random vector with respect to an order-( ) risk-sensitive criterion are studied in this note. More precisely, we prove the existence of a unique risk-sensitive estimate provided 0 and 1. For the remaining ca...

The results in this paper are part of a program to understand to what extent one can use mean curvature data to determine the shape of a surface in R. The first section of the paper presents some new results on a uniqueness problem suggested by Bonnet. A generic immersion is uniquely determined up to a rigid motion by its first fundamental form and its mean curvature function, but there are som...

In optical tomography, conventionally the diffusion approximation (DA) to the radiative transport equation (RTE) with a constant refractive index is used. The existence, uniqueness, and non-uniqueness of the forward and the inverse problem using conventional DA has been studied in the past. In this report, we investigate the existence, uniqueness, and non-uniqueness of optical tomography forwar...

The existence and uniqueness of a periodic solution of the system of differential equations d dt x(t) = A(t)x(t − ) are proved. In particular the Krasnoselskii’s fixed point theorem and the contraction mapping principle are used in the analysis. In addition, the notion of fundamental matrix solution coupled with Floquet theory is also employed.  

This paper proves the existence and uniqueness of quadratic mean almost periodic mild so-lutions for a class of stochastic dierential equations in a real separable Hilbert space. Themain technique is based upon an appropriate composition theorem combined with the Banachcontraction mapping principle and an analytic semigroup of linear operators.  

In this paper, a new set of spline functions called ``Flat End Fuzzy Spline" is defined to interpolate given fuzzy data. Some important theorems on these splines together with their existence and uniqueness properties are discussed. Then numerical examples are presented to illustrate the differences between of using our spline and other interpolations that have been studied before.

In this paper the fixed point theorem of Schauder is used to prove the existence of a continuous solution of the nonlinear fuzzy Volterra integral equations. Then using some conditions the uniqueness of the solution is investigated.