Papers by Keyword: Boundary Value Problem

Abstract: In this paper we consider the boundary value problem and optimal control problem for nonlinear convection-diffusion-reaction equation, in which reaction coefficient depends on concentration of polluting substance. Sufficiently common type of nonlinear dependence is investigated, within which solvability of boundary value and optimal control problem is proved, and local uniqueness of weak solution is obtained.

Abstract: In this paper control problems for 2-D Helmholtz equation are formulated and investigated. These problems are associated with developing technology of acoustic cloaking. Helmholtz equation is considered in an unbounded domain with the impedance boundary condition. The role of control in control problems under study is played by surface impedance.

Abstract: The Cauchy function and characteristic series were applied to solve the boundary value problem of free transverse vibrations of vertically mounted, elastically supported tapered cantilever beams. A concentrated mass was attached at the same distance from the base. The beams were subjected to universal axial loads - conservative and follow wing tangential forces - and distributed loads along the cantilever length. The general form of characteristic equation was obtained taking into account the shape of the tapered cantilever, elastic foundation and nonhomogeneous material. Bernstein-Kieropian double estimators of natural frequency were calculated based on free coefficients of the characteristic series. Good agreement was obtained between the calculated natural frequency results and the exact values available in the literature.

Abstract: In this paper, by using Leggett-Williams fixed point theorem, we will study the existence of positive solutions for a class of multi-point boundary value problems of fractional differential equation on infinite interval.

Abstract: In this paper we investigate the existence of positive solution of the following discrete two-order three-point boundary value problemWherandis sign-changing on . By using the fixed-point index theory, the existence of positive solutions for the above boundary value problem is obtained.

Abstract: This paper studies the seepage flow mathematical model of three-area composite reservoir under three kinds of outer boundary conditions (infinite boundary, constant pressure boundary and closed boundary), in which influences of well-bore storage and skin factor are not taken into consideration. On the basic of theory of similar structure of solution of boundary value problem of differential equation, this paper obtain the solution of the seepage flow model of three-area composite reservoir. The study is not only conducive to further analyze the inherent law of the solution and solve corresponding application problems, but also easy to compile corresponding analysis software.

Abstract: : In the framework of Darcy's law of filtration the investigation results of one class of boundary value problems of the steady-state filtration theory in porous ground base are presented. The plane mixed bounadry value problems on the structural analysis of hydrotechnical con­struction of dam type on filtrating ground base in the form of a layer of finite or infinite thickness are considered. The coefficient of filtration is assumed to be constant, piecewise constant, or changing by the depth of base according to the exponential law, the property of anisotropy of filtration is also taken into account. Axis-symmetric and three-dimentional boundary value problems of the theory of steady-state fluid filtration in a three-dimentional layer of a finite or infinite thickness are discussed. These problems are of the type of Lamb well-known hydrodynamic problems in the theory of steady-state flow of the ideal fluid, when through the circular or rectangular openeing of a rigid screen on the upper bound of the layer the liquid with a definite vertical velocity or with a definite pressure is injected into porous ground base. Here, the fields of velocities and pressures in the layer, as well as flow rates of liquid through the certain sections of the ground base are determined.

Abstract: In this paper we investigate the existence of positive solution of the following nonlinear discrete third-order two-point boundary value problem. whereis continuous and there existssuch that . Our approach relies on the Krasnosel'skii fixed point theorem. An example is given to demonstrate the application of the theorem obtained.

Abstract: The similar structure of solution for the boundary value problem of second order linear homogeneous differential equation has been studied. Based on the analysis of the relationship between similar structure of solution, its kernel function, the equation and boundary conditions, similar constructive method (shortened as SCM) of solution is obtained. According to the SCM, the similar structure of solution and its kernel function are constructed for the mathematical model of homogeneous reservoir which considers the influence of bottom-hole storage and skin effect under the infinite outer boundary condition. The SCM is a new and innovative way to solve boundary value problem of differential equation and seepage flow theory, which is especially used in Petroleum Engineering.

Abstract: This paper mainly concerns the uniqueness of solutions for a fourth order boundary value problem. By virtue of Browder theorem, the main result is obtained when the nonlinearity term f satisfies the Lipschitz condition. The result is new and complement of some previously known results.