A characterization of nonlinear φ-accretive operators

Let E be a Banach space and E(–,] a proper lower semi-continuous convex function. The main purpose of this paper is to characterize those m-accretive operators AE x E that are also -accretive. This is done by using the semigroup S generated by -A, and by first establishing a necessary and sufficient condition for to be a Lyapunov function for S. We also obtain similar results for accretive operators that are not necessarily m-accretive, and deduce invariance and order-preserving criteria for nonlinear semigroups.This research was partially supported by the National Science Foundation under Grant MCS-8102086.     

Parameter estimation in nonlinear evolution equations

We develop a convergence theory for identifying parameters in a general class of nonau-

tonomous nonlinear evolution equations. An application of this theory to a nonlinear reaction diffusion equation is presented.     

Shape Gradient for Isogeometric Structural Design

The transfer of geometrical data from CAD (Computer Aided Design) to FEA (Finite-Element Analysis) is a bottleneck of automated design optimization procedures, yielding a loss of accuracy and cumbersome software couplings. Isogeometric analysis methods propose a new paradigm that allows one to overcome these difficulties by using a unique geometrical representation, yielding a direct relationship between geometry and analysis. In this study, in the framework of linear elasticity problems, we investigate its use for sensitivity analysis and, more specifically, shape gradient computations.     

A Denjoy–Wolff theorem for compact holomorphic mappings in reflexive Banach spaces

Using the Kobayashi distance, we establish a Denjoy–Wolff theorem for compact holomorphic self-mappings of a bounded and strictly convex domain in a complex reflexive Banach space.     

Iterative Averaging of Entropic Projections for Solving Stochastic Convex Feasibility Problems

The problem considered in this paper is that of finding a point which iscommon to almost all the members of a measurable family of closed convexsubsets of R₊₊ ⁿ , provided that such a point exists.The main results show that this problem can be solved by an iterative methodessentially based on averaging at each step the Bregman projections withrespect to f(x)=_i=1 ⁿx_i· ln x_i ofthe current iterate onto the given sets.