This work is concerned with the equilibrium configurations of elastic structuresin contact with Coulomb friction. We obtain a variational formulation of thisequilibrium problem. Then we propose sufficient conditions for the existence ofan infinity of equilibrium configurations with arbitrary small frictioncoefficients. We illustrate the result in two space dimensions with asimple example.

In this work we consider a stabilized Lagrange multiplier method in order toapproximate the Coulomb frictional contact model in linear elastostatics. Theparticularity of the method is that no discrete inf-sup condition is needed. Westudy the existence and the uniqueness of solution of the discrete problem.

The paper is devoted to mathematical modelling and numerical computations of anonstationaryfree boundary problem. The model is based on processes of molecular diffusion ofsomeproducts of chemical decomposition of a solid organic substance concentrated inbottom sediments.It takes into account non-stationary multi-component and multi-stage chemicaldecomposition oforganic substances and the processes of sorption desorption under aerobic andanaerobic conditions.Such a model allows one to obtain quantitative estimates of incoming soluteorganicsubstances of anthropogenic origin having different molecular weights from thebottom sedimentsinto water and to study the influence of seasonal variations of theconcentration of solute oxygenin the near-bottom water on the direction of exchange processes in the system“waterbottom”.
Identification of parameters of the mathematical model with the use ofexperimental data andwith the employment of a priori information of the model's structure is carriedout. Comparisonof the numerical simulations with experimental data is conducted to the end ofverification ofefficiency and plausibility of the proposed mathematical model of secondarypollution. It impliesassessment of water quality on account of the processes of exchange in thesystem “waterbottom”.The results of computations of non-stationary fluxes at the boundary“waterbottom” are analyzed.A model example is used to estimate the potentials of the biogenic load on thewater reservoir.

We study the growth rate of a cell population that follows anage-structured PDE with time-periodic coefficients. Our motivationcomes from the comparison between experimental tumor growth curvesin mice endowed with intact or disrupted circadian clocks,known to exert their influence on the cell division cycle.We compare the growth rate of the model controlled by a time-periodiccontrol on its coefficients with the growth rate of stationarymodels of the same nature, but with averaged coefficients. We firstly derive a delay differential equation which allows us to proveseveral inequalities and equalities on the growth rates. We alsodiscuss about the necessity to take into account the structure ofthe cell division cycle for chronotherapy modeling. Numerical simulationsillustrate the results.

In this note we give a result of convergence when time goes to infinity for aquasi static linear elastic model, the elastic tensor of which vanishes atinfinity. This method is applied to segmentation of medical images, and improvesthe 'elastic deformable template' model introduced previously.

The paper is devoted to mathematical modelling of erythropoiesis, production of red blood cells in the bone marrow. We discuss intra-cellular regulatory networks which determine self-renewal and differentiation of erythroid progenitors. In the case of excessive self-renewal, immature cells can fill the bone marrow resulting in the development of leukemia. We introduce a parameter characterizing the strength of mutation. Depending on its value, leukemia will or will not develop. The simplest model of treatment of acute myeloid leukemia with chemotherapy allows us to determine the conditions of successful treatment or of its failure. We show that insufficient treatment can worsen the situation. In some cases curing may not be possible even without resistance to treatment. Modelling presented in this work is based on ordinary differential equations, reaction-diffusion systems and individual based approach.

The flow trough the Strait of Gibraltar could be analyzed as a problem oftwo-layerhydraulic exchange between the Atlantic ocean and the Mediterranean sea. Theshallow waterequations in both layers coupled together are an important tool to simulate thisphenomenon. Inthis paper we perform an upwind schemes for hyperbolic equations based on theRoe approximateRiemann solver, to study the resulting model. The main goal assigned was topredict the locationof the interface between the two layers. Therefore the computational resultsobtained are comparedto previous results and experiments.

In this work we deal with the design of the robust feedback control ofwastewater treatmentsystem, namely the activated sludge process. This problem is formulated by anonlinearordinary differential system. On one hand, we develop a robust analysis when thespecific growthfunction of the bacterium μ is not well known. On the other hand, when alsothe substrate concentrationin the feed stream s in is unknown, we provide an observer of system andpropose a designof robust feedback control in term of recycle rate, in order to keep thepollutant concentration lowerthan an allowed maximum level s d .

The paper considers a methodology of mathematical modeling ofecological-economicprocesses at the regional level. The basis of the model is formed by equations,which describetwo interacting blocks: economic and ecological ones. Equations of the economicblock are representedby relations of generalized inter-branch balance, while the ecological part isdescribedin terms of differential equations with deviations with respect to some givenstate of natural resources.Issues of i) information support of the model, ii) techniques used foridentification of thecoefficients, iii) scenario analysis and iv) forecasting are analyzed.

This paper is concerned with the methods of mathematical modeling of thesocio-economicdevelopment of regions. The objective of this study is to analyze and assess thesocio-economicpotential of the territory having regard to its individual socio-economic andeconomic-geographicalcharacteristics. The territory's individual characteristics, in turn, aretreated as invariantconditions of its development. The study territory includes regions and federaldistricts of theRussian Federation.
An assessment of the regions' development potential is made from the perspectiveof analyzingtheir current socio-economic situation for the time interval 1999-2002 takenfrom official statisticalhandbooks. To accomplish this, a special-purpose mathematical model is developedin the formof a hierarchical fractal indicative function relating the generalized indicatorcharacterizing theregions' development potential, or the “indicated” (that which is indicatedversus indicator), to theparticular socio-economic characteristics of the territory, or the developmentindicators of the localeconomy, via the model coefficients which is termed regulators.
As a result, the economic-mathematical model is generated in the form of anindicative functioncharacterizing the current socio-economic situation of the regions and federaldistricts of Russiaon different levels of economic organization (from local and regional tonational). It reflects appropriatelyand dramatically the specific character of the region's socio-economic potentialby theexample of the connection of investments with the volumes of production. Themodel permitsthe position of the regions and districts to be identified in the system ofinter-regional and nationalsocio-economic links and economic-geographical conditions of development. Theresultsderived from modeling the socio-economic development potential of Russia'sregions have beenused to construct the control surface of the country's economy characterizingthe changes in the development potential of the federal districts toward itsdecrease.