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Ecological-Economic Model of the Region: Information Technology, Forecasting and Optimal Control

V. Gurman, V. Baturin (2009)

Mathematical Modelling of Natural Phenomena

The paper considers a methodology of mathematical modeling of ecological-economic processes at the regional level. The basis of the model is formed by equations, which describe two interacting blocks: economic and ecological ones. Equations of the economic block are represented by relations of generalized inter-branch balance, while the ecological part is described in terms of differential equations with deviations with respect to some given state of natural resources. Issues of i) information...

Economic equilibrium through variational inequalities

Magdalena Nockowska-Rosiak (2009)

Applicationes Mathematicae

The purpose of this paper is to present an alternative proof of the existence of the Walrasian equilibrium for the Arrow-Debreu-McKenzie model by the variational inequality technique. Moreover, examples of the generalized Arrow-Debreu-McKenzie model are given in which the price vector can reach the boundary of the orthant allowing a commodity to be of price zero at equilibrium. In such a case its supply exceeds demand. It is worth mentioning that utility functions in this model are allowed not to...

Editorial

Olga Krupková (2010)

Communications in Mathematics

Effective energy integral functionals for thin films with bending moment in the Orlicz-Sobolev space setting

Włodzimierz Laskowski, Hôǹg Thái Nguyêñ (2014)

Banach Center Publications

In this paper we deal with the energy functionals for the elastic thin film ω ⊂ ℝ² involving the bending moments. The effective energy functional is obtained by Γ-convergence and 3D-2D dimension reduction techniques. Then we prove the existence of minimizers of the film energy functional. These results are proved in the case when the energy density function has the growth prescribed by an Orlicz convex function M. Here M is assumed to be non-power-growth-type and to satisfy the conditions Δ₂ and...

Effective energy integral functionals for thin films with three dimensional bending moment in the Orlicz-Sobolev space setting

Włodzimierz Laskowski, Hong Thai Nguyen (2016)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we consider an elastic thin film ω ⊂ ℝ² with the bending moment depending also on the third thickness variable. The effective energy functional defined on the Orlicz-Sobolev space over ω is described by Γ-convergence and 3D-2D dimension reduction techniques. Then we prove the existence of minimizers of the film energy functional. These results are proved in the case when the energy density function has the growth prescribed by an Orlicz convex function M. Here M is assumed to be non-power-growth-type...

Efficient algorithm to solve optimal boundary control problem for Burgers' equation

Alaeddin Malek, Roghayeh Ebrahim Nataj, Mohamad Javad Yazdanpanah (2012)

Kybernetika

In this paper, we propose a novel algorithm for solving an optimal boundary control problem of the Burgers' equation. The solving method is based on the transformation of the original problem into a homogeneous boundary conditions problem. This transforms the original problem into an optimal distributed control problem. The modal expansion technique is applied to the distributed control problem of the Burgers' equation to generate a low-dimensional dynamical system. The control parametrization method...

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