Authors: Guang Shan Xu, Zhong Tai Ma

Abstract: In this paper, the problem of non-smooth properties for a type of general second order parabolic type equation is discussed and the result-------there are C∞-functions f for which we consider the equation that has no C2-solutions is proved by using a method of function construction, moreover, the dependent relations between the solution u and the diffusion term f is given.

877

Authors: Shu Xian Deng, Zhi Wei Wang

Abstract: In this paper, we shall research on a class of thermo-viscous-elastic anisotropic dissipative material system equation. The analysis semi-group theory and two-dimensional singular integral operator identical relations are used in this paper; the equations denoted by some singular integral operator equalities are studied in two-dimensional round field. We shall push out the properties of the equations, the necessary and sufficient conditions of solvability. Furthermore, the formulas of their exponent operation are pushed out too.

126

Authors: Ildar B. Badriev, Victor V. Banderov, O.A. Zadvornov

Abstract: We consider a spatial equilibrium problem of a soft network shell in the presence of several external point loads concentrated at some pairwise distinct points. A generalized statement of the problem is formulated in the form of integral identity. Then we introduce an auxiliary problem with the right-hand side given by the delta function. For the auxiliary problem we are able to find the solution in an explicit form. Due to this, the generalized statement of the problem under consideration is reduced to finding the solution of the operator equation. We establish the properties of the operator of this equation (boundedness, continuity, monotonicity, and coercitivity), which makes it possible to apply known general results from the theory of monotone operatorsfor the proof of the existence theorem. It is proved that the set of solutions of the generalized problem is non-empty, convex, and closed.

188

Authors: Roman Brizitskii, Dmitry Tereshko

Abstract: The new control problems for the stationary magnetohydrodynamics equations under inhomogeneous boundary conditions for the magnetic field are considered. In these problems we use velocity and magnetic field boundary controls to minimize functionals depended on velocity and pressure. We study uniqueness and stability of solutions to these control problems and discuss some computational results.

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