The problem of determining the stress-strain state rigidly fixed sandwich plate with transversely soft core in the presence of constraints (i.e., material nonlinearity) corresponding to the ideal elastic-plastic model for the core material is considered. Solvability of the generalized statement of the problem as a problem of finding the saddle point of some functionals is investigated.

517.958 In the present article we conduct a study of the convergence of a recursive process for solving a stationary problem of the theory of soft shells that arises in the description of the uniaxial static state of a soft shell [1][2][3]. Mathematically the problem is stated in the form of an equation with a pseudomonotone operator [4]. We prove an existence theorem for the solution of this equation. To solve the problem we propose a two-tiered recursive process. We obtain an a priori estimate for the sequence of recursive approximations, on the basis of which we establish tl~. existence of a subsequence of the recursive approximations that converges weakly to a certain solution of this problem. In studying the convergence of the recursive process we use the equivalence of the original equation to a variational inequality.1. We consider the boundary-value problem77 ( (6)Conditions (2)- (5) mean that g(~2)~ is an absolutely continuous function that is nondecreasing for >_ 0 and linear at infinity.We assume also that the functions ql and q2 satisfy the conditionsLet V =vd~l)(0,1)x l~d~l)(0, 1), V = W2(-1)(0, 1) x W(-1)(0,1), and let (.,.) be the duality relation between V and V*. We introduce the operators A0 : V ---* V*, L : V ~ V* generated respectively by the forms fo l d~ dfi d~?~01 du

Decarbonization of the world economy is one of the main trends in global development of the last decade. The beginning of the transition of the world economy to green energy poses new tasks and challenges for the geological exploration industry as well as for the fuel and energy complex. Currently, the most demanded energy-chemical resources are oil, natural gas and, to a lesser extent, coal. Their production has approached the maximum possible level and in the near future will inevitably begin to decline. However, due to large investments and highly efficient technologies, the process of switching to alternative energy sources may drag on for a long period, during which traditional hydrocarbons will remain the basis of the energy sector in many countries. The share of hard-to-recover reserves in the world is constantly growing; in Russia, it currently exceeds 65%. Hard-to-recover reserves include, in particular, reserves of highviscosity oils and bitumen (with a viscosity of more than 30 mPa·s). The article discusses the prospects and possible ways of developing bitumen and coal deposits within the Volga-Ural oil and gas basin. Keywords: decarbonization; natural bitumen; heavy oil; coal seams; thermal treatment.

We consider a generalization of the algorithm of II'ichev-Postolovskii [1] for computing flow detachment from an arbitrary closed contour. The incompressible plane flow is assumed uniform at infinity and the immersed contour is assumed smooth. The detached boundary layer -the layer of free shear flow -is treated as a sheet of vorticity and a single detachment point is assumed for simplicity.

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