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Том 228, № 4 (2018)
- Год: 2018
- Статей: 11
- URL: https://bakhtiniada.ru/1072-3374/issue/view/14879
Article
335-346
347-356
Numerical Modeling of Gas-Liquid Compressible Pipe Flow Based on the Theory of Thermodynamically Compatible Systems
Аннотация
Based on the theory of thermodynamically compatible systems, we formulate the governing equations of a gas-liquid compressible pipe flow and develop the Runge–Kutta–TVD and Runge–Kutta–WENO high accuracy methods. The computational model is used to solve a series of test cases demonstrating its efficiency and capability to be applied to slug flows modeling.
357-371
Galerkin Method for Semilinear Parabolic Equation with Varying Time Direction
Аннотация
We establish the unique solvability of the first boundary value problem for a semilinear second order parabolic equation with varying time direction by using a modified Galerkin method and the regularization method. We obtain a priori error estimates for approximate solutions.
372-379
Analytic in a Sector Resolving Families of Operators for Degenerate Evolution Fractional Equations
Аннотация
We introduce a class of pairs of operators defining a linear homogeneous degenerate evolution fractional differential equation in a Banach space. Reflexive Banach spaces are represented as the direct sums of the phase space of the equation and the kernel of the operator at the fractional derivative. In a sector of the complex plane containing the positive half-axis, we construct an analytic family of resolving operators that degenerate only on the kernel. The results are used in the study of the solvability of initial-boundary value problems for partial differential equations containing fractional time-derivatives and polynomials in the Laplace operator with respect to the spatial variable.
380-394
Qualitative Properties of Solutions to Elliptic Equations with Nonpower Nonlinearities in ℝn
Аннотация
We consider a class of anisotropic elliptic equations with nonpower nonlinearities. We establish the existence of a solution in the local Sobolev–Orlicz spaces without conditions on the data growth at infinity. We find sufficient uniqueness conditions, obtain estimates characterizing the behavior of the solution at infinity, and prove the continuous dependence of the solution on the right-hand side of the equation.
395-408
Optimal Control of the Rigid Inclusion Size in the Problem of Equilibrium of Inhomogeneous Timoshenko Type Plates Containing Cracks
Аннотация
We consider the equilibrium problem for plates with cracks located along rigid inclusions and analyze the dependence of the solution and the derivative of the energy functional on variations of the inclusion size. We establish the solvability of the optimal control problem, where the quality functional is given by the derivative of the energy functional, whereas the control parameter correspond to the inclusion size. A similar analysis is performed for the equilibrium problems for inhomogeneous plates with rigid delaminated inclusions.
409-420
Boundary Value Problems for Nonclassical Systems of Second Order Differential Equations
Аннотация
We study boundary value problems for systems of second order differential equations with principal part in the form of the squared first order differential operator. We establish the unique solvability of the boundary value problem for a nonclassical system in the plane, which can be regarded as the Riemann–Hilbert problem with discontinuous boundary conditions. Similar problems are considered in the space.
421-430
Solvability of Nonlinear Inverse Problem for Hyperbolic Equation
Аннотация
We consider the nonlinear inverse problem for a second order hyperbolic equation with unknown coefficient depending on the time. We establish the existence and uniqueness of regular solutions which are used for constructing a soltuion to the inverse problem under consideration.
431-448
Classical Solvability of the Radial Viscous Fingering Problem in a Hele–Shaw Cell with Surface Tension
Аннотация
We consider the one-phase problem on radial viscous fingering structures in a Hele–Shaw cell with surface tension. This problem is a nonlinear free-boundary problem for elliptic equations. Unlike the Stefan problem for the heat equation, we deal with a problem of hydrodynamic type. We establish the classical solvability of the one-phase Hele–Shaw problem with radial geometry by using the same method as that used for the Stefan problem and justifying the vanishing coefficient of the time-derivative in the parabolic equation.
449-462
Influence of Gradient Terms on the Existence of Solutions to the Dirichlet Problem for p-Laplacian
Аннотация
We study the Dirichlet problem for the inhomogeneous p-Laplace equation with a nonlinear source and a gradient term. We investigate the influence of the gradient term on the existence of radially symmetric solutions. Sufficient conditions for the existence of solutions are explicetly given in terms of the data of the problem.
463-474