Search results for " Projection operator"
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Fixed point iterative schemes for variational inequality problems
2018
In a wide class of evolutionary processes, the problem of computing the solutions of an initial value problem is encountered. Here, we consider projected dynamical systems in the sense of \cite{Daniele} and references therein. Precisely, a projected dynamical system is an operator which solves the initial value problem: \begin{equation}\label{PDS}\frac{dx(t)}{dt}= \Pi_{\mathbb{K}}\left(x(t),-F(x(t))\right), \quad x(0)=x_0 \in \mathbb{K}, \, t \in [0,+\infty[,\tag{P}\end{equation} where $\mathbb{K}$ is a convex polyhedral set in $\mathbb{R}^n$, $F: \mathbb{K} \to \mathbb{R}^n$ and $\Pi_{\mathbb{K}}: \mathbb{R} \times \mathbb{K} \to \mathbb{R}^n$ is given as follows $\Pi_{\mathbb{K}}(x,-F(x))…
On the generalization of the Boltzmann equation
1974
Starting from the Liouville equation and making use of projection operator techniques we obtain a compact equation for the rate of change of then-particle momentum distribution function to any order in the density. This equation is exact in the thermodynamic limit. The terms up to second order in the density are studied and expressions are given for the errors committed when one makes the usual hypothesis to derive generalized Boltzmann equations. Finally the Choh-Uhlenbeck operator is obtained under additional assumptions.