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Khalida Inayat Noor is a Pakistani mathematician who was awarded with Pride of Performance award by the President of Pakistan in 2011. [1] Her research topics include mathematical analysis , variational inequalities , and integral operators .
The first problem involving a variational inequality was the Signorini problem, posed by Antonio Signorini in 1959 and solved by Gaetano Fichera in 1963, according to the references (Antman 1983, pp. 282–284) and (Fichera 1995): the first papers of the theory were (Fichera 1963) and (Fichera 1964a), (Fichera 1964b).
The obstacle problem is a classic motivating example in the mathematical study of variational inequalities and free boundary problems.The problem is to find the equilibrium position of an elastic membrane whose boundary is held fixed, and which is constrained to lie above a given obstacle.
Finite-Dimensional Variational Inequalities and Complementarity Problems, Volume I This page was last edited on 27 January 2022, at 06:45 (UTC). Text ...
Differential inclusions arise in many situations including differential variational inequalities, projected dynamical systems, Moreau's sweeping process, linear and nonlinear complementarity dynamical systems, discontinuous ordinary differential equations, switching dynamical systems, and fuzzy set arithmetic.
Many free boundary problems can profitably be viewed as variational inequalities for the sake of analysis. To illustrate this point, we first turn to the minimization of a function F {\displaystyle F} of n {\displaystyle n} real variables over a convex set C {\displaystyle C} ; the minimizer x {\displaystyle x} is characterized by the condition
The statement of the problem involves not only equalities but also inequalities, and it is not a priori known what of the two sets of boundary conditions is satisfied at each point. Signorini asked to determine if the problem is well-posed or not in a physical sense, i.e. if its solution exists and is unique or not: he explicitly invited young ...
There are mainly two kinds of methods to model the unilateral constraints. The first kind is based on smooth contact dynamics, including methods using Hertz's models, penalty methods, and some regularization force models, while the second kind is based on the non-smooth contact dynamics, which models the system with unilateral contacts as variational inequalities.