Showing papers in "Boundary Value Problems in 2010"
TL;DR: In this paper, a new conservative finite difference scheme is presented for an initial-boundary value problem of the general Rosenau-RLW equation, which is proved to be uniquely solvable, unconditionally stable, and second-order convergent.
Abstract: A new conservative finite difference scheme is presented for an initial-boundary value problem of the general Rosenau-RLW equation. Existence of its difference solutions are proved by Brouwer fixed point theorem. It is proved by the discrete energy method that the scheme is uniquely solvable, unconditionally stable, and second-order convergent. Numerical examples show the efficiency of the scheme.
57 citations
TL;DR: In this paper, the problem of magnetohydrodynamic flow and heat transfer of a viscous, incompressible, and electrically conducting fluid past a semi-infinite unsteady stretching sheet is analyzed numerically.
Abstract: The problem of magnetohydrodynamic flow and heat transfer of a viscous, incompressible, and electrically conducting fluid past a semi-infinite unsteady stretching sheet is analyzed numerically. The problem was studied under the effects of Hall currents, variable viscosity, and variable thermal diffusivity. Using a similarity transformation, the governing fundamental equations are approximated by a system of nonlinear ordinary differential equations. The resultant system of ordinary differential equations is then solved numerically by the successive linearization method together with the Chebyshev pseudospectral method. Details of the velocity and temperature fields as well as the local skin friction and the local Nusselt number for various values of the parameters of the problem are presented. It is noted that the axial velocity decreases with increasing the values of the unsteadiness parameter, variable viscosity parameter, or the Hartmann number, while the transverse velocity increases as the Hartmann number increases. Due to increases in thermal diffusivity parameter, temperature is found to increase.
56 citations
TL;DR: In this article, the classical von Karman equations governing the boundary layer flow induced by a rotating disk are solved using the spectral homotopy analysis method and a novel successive linearisation method, combining nonperturbation techniques with the Chebyshev spectral collocation method.
Abstract: The classical von Karman equations governing the boundary layer flow induced by a rotating disk are solved using the spectral homotopy analysis method and a novel successive linearisation method The methods combine nonperturbation techniques with the Chebyshev spectral collocation method, and this study seeks to show the accuracy and reliability of the two methods in finding solutions of nonlinear systems of equations The rapid convergence of the methods is determined by comparing the current results with numerical results and previous results in the literature
47 citations
TL;DR: In this paper, two energy conservative finite difference schemes are proposed for the generalized Rosenau equation and stability, convergence, and priori error estimation of the scheme are proved using energy method.
Abstract: Numerical solutions for generalized Rosenau equation are considered and two energy conservative finite difference schemes are proposed. Existence of the solutions for the difference scheme has been shown. Stability, convergence, and priori error estimate of the scheme are proved using energy method. Numerical results demonstrate that two schemes are efficient and reliable.
42 citations
TL;DR: In this article, a stochastic system of evolution partial differential equations for the turbulent flows of a second grade fluid filling a bounded domain of space is investigated. And the global existence of a probabilistic weak solution is established.
Abstract: We initiate the investigation of a stochastic system of evolution partial differential equations modelling the turbulent flows of a second grade fluid filling a bounded domain of . We establish the global existence of a probabilistic weak solution.
39 citations
TL;DR: In this article, the authors prove the existence and uniqueness of a strong solution to the stochastic Navier-Stokes equations under appropriate conditions on the data using the Galerkin approximation scheme.
Abstract: We prove the existence and uniqueness of strong solution to the stochastic Leray-
equations under appropriate conditions on the data. This is achieved by means of the Galerkin approximation scheme. We also study the asymptotic behaviour of the strong solution as alpha goes to zero. We show that a sequence of strong solutions converges in appropriate topologies to weak solutions of the 3D stochastic Navier-Stokes equations.
31 citations
TL;DR: In this article, the authors studied conditions on so that the operator admits the maximum principle or the antimaximum principle with respect to the periodic boundary condition, by exploiting Green functions, eigenvalues, rotation numbers, and their estimates.
Abstract: Given a periodic, integrable potential , we will study conditions on so that the operator admits the maximum principle or the antimaximum principle with respect to the periodic boundary condition. By exploiting Green functions, eigenvalues, rotation numbers, and their estimates, we will give several optimal conditions.
27 citations
TL;DR: In this article, an inverse scattering problem for a discontinuous Sturm-Liouville equation on the half-line with a linear spectral parameter in the boundary condition is considered and a new fundamental equation is derived.
Abstract: An inverse scattering problem is considered for a discontinuous Sturm-Liouville equation on the half-line with a linear spectral parameter in the boundary condition. The scattering data of the problem are defined and a new fundamental equation is derived, which is different from the classical Marchenko equation. With help of this fundamental equation, in terms of the scattering data, the potential is recovered uniquely.
26 citations
TL;DR: In this paper, the authors considered the Cauchy problem for nonstationary 1D flow of a compressible viscous and heat-conducting micropolar fluid, assuming that it is in the thermodynamical sense perfect and polytropic.
Abstract: We consider the Cauchy problem for nonstationary 1D flow of a compressible viscous and heat-conducting micropolar fluid, assuming that it is in the thermodynamical sense perfect and polytropic. This problem has a unique generalized solution on for each . Supposing that the initial functions are small perturbations of the constants we derive a priori estimates for the solution independent of , which we use in proving of the stabilization of the solution.
26 citations
TL;DR: In this article, the existence of positive solutions to the three-point integral boundary value problem was studied and it was shown that there exists at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem in cones.
Abstract: We study the existence of positive solutions to the three-point integral boundary value problem , , , , where and . We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem in cones.
24 citations
TL;DR: In this paper, the multiplicity of solutions for Kirchhoff type problems was studied by using variational methods, and the existence results of two nontrivial solutions and infinite many solutions were obtained.
Abstract: By using variational methods, we study the multiplicity of solutions for Kirchhoff type problems , in ; , on . Existence results of two nontrivial solutions and infinite many solutions are obtained.
TL;DR: In this paper, the Guo-Krasnoselskii fixed-point theorem was used to obtain sufficient conditions for the existence and nonexistence of monotone positive solution to the third-order boundary value problem.
Abstract: This paper is concerned with the following third-order boundary value problem with integral boundary conditions , where and . By using the Guo-Krasnoselskii fixed-point theorem, some sufficient conditions are obtained for the existence and nonexistence of monotone positive solution to the above problem.
TL;DR: In this article, the existence of distinct pairs of nontrivial solutions for impulsive differential equations with Dirichlet boundary conditions was studied using variational methods and critical point theory. But the existence was not proved.
Abstract: We study the existence of distinct pairs of nontrivial solutions for impulsive differential equations with Dirichlet boundary conditions by using variational methods and critical point theory.
TL;DR: In this article, the authors give a complete quantification of their results and clarify the sharp constants for the coefficients of the logarithmic terms in Besov and Triebel-Lizorkin spaces.
Abstract: The present paper concerns the Sobolev embedding in the endpoint case. It is known that the embedding fails for . Brezis-Gallouet-Wainger and some other authors quantified why this embedding fails by means of the Holder-Zygmund norm. In the present paper we will give a complete quantification of their results and clarify the sharp constants for the coefficients of the logarithmic terms in Besov and Triebel-Lizorkin spaces.
TL;DR: In this paper, the exponential-type stability of linear neutral delay differential systems with constant coefficients using Lyapunov-Krasovskii type functionals was investigated and conditions sufficient for the stability were formulated in terms of positivity of auxiliary matrices.
Abstract: This paper investigates the exponential-type stability of linear neutral delay differential systems with constant coefficients using Lyapunov-Krasovskii type functionals, more general than those reported in the literature. Delay-dependent conditions sufficient for the stability are formulated in terms of positivity of auxiliary matrices. The approach developed is used to characterize the decay of solutions (by inequalities for the norm of an arbitrary solution and its derivative) in the case of stability, as well as in a general case. Illustrative examples are shown and comparisons with known results are given.
TL;DR: In this paper, the authors considered a nonself-adjoint fourth-order differential operator with the periodic boundary conditions and obtained new asymptotic formulas for eigenvalues and eigenfunctions.
Abstract: In the present paper, we consider a nonself-adjoint fourth-order differential operator with the periodic boundary conditions. We compute new accurate asymptotic expression of the fundamental solutions of the given equation. Then, we obtain new accurate asymptotic formulas for eigenvalues and eigenfunctions.
TL;DR: In this paper, the existence of antiperiodic solutions for Lienard-type and Duffing-type differential equations with -Laplacian operator has been studied by using degree theory.
Abstract: The existence of antiperiodic solutions for Lienard-type and Duffing-type differential equations with -Laplacian operator has been studied by using degree theory. The results obtained improve and enrich some known works to some extent.
TL;DR: In this article, the authors investigated the asymptotic behavior of eigenvalues and eigenfunctions of Stekloff eigenvalue problems in perforated domains.
Abstract: By means of the two-scale convergence method, we investigate the asymptotic behavior of eigenvalues and eigenfunctions of Stekloff eigenvalue problems in perforated domains. We prove a concise and precise homogenization result including convergence of gradients of eigenfunctions which improves the understanding of the asymptotic behavior of eigenfunctions. It is also justified that the natural local problem is not an eigenvalue problem.
TL;DR: In this paper, the variational iteration method and the homotopy perturbation method were applied to solve Sturm-Liouville eigenvalue and boundary value problems.
Abstract: We applied the variational iteration method and the homotopy perturbation method to solve Sturm-Liouville eigenvalue and boundary value problems. The main advantage of these methods is the flexibility to give approximate and exact solutions to both linear and nonlinear problems without linearization or discretization. The results show that both methods are simple and effective.
TL;DR: In this paper, a polynomial-type Jost solution of the self-adjoint discrete Dirac system was found, and analytical properties and asymptotic behaviour of the Jost Solution were investigated.
Abstract: We find polynomial-type Jost solution of the self-adjoint discrete Dirac systems. Then we investigate analytical properties and asymptotic behaviour of the Jost solution. Using the Weyl compact perturbation theorem, we prove that discrete Dirac system has the continuous spectrum filling the segment [-2,2]. We also study the eigenvalues of the Dirac system. In particular, we prove that the Dirac system has a finite number of simple real eigenvalues.
TL;DR: In this article, a finite difference method for dissipative symmetric regularized long wave equations with damping term was proposed and proved to be second-order convergence and unconditionally stable.
Abstract: We study the initial-boundary problem of dissipative symmetric regularized long wave equations with damping term by finite difference method. A linear three-level implicit finite difference scheme is designed. Existence and uniqueness of numerical solutions are derived. It is proved that the finite difference scheme is of second-order convergence and unconditionally stable by the discrete energy method. Numerical simulations verify that the method is accurate and efficient.
TL;DR: In this paper, the authors discuss how homology computation can be exploited in computational electromagnetism and present various cellular mesh reduction techniques, which enable the computation of generators of homology spaces in an acceptable time.
Abstract: We discuss how homology computation can be exploited in computational electromagnetism. We represent various cellular mesh reduction techniques, which enable the computation of generators of homology spaces in an acceptable time. Furthermore, we show how the generators can be used for setting up and analysis of an electromagnetic boundary value problem. The aim is to provide a rationale for homology computation in electromagnetic modeling software.
TL;DR: In this paper, a computational model is developed to analyze the unsteady flow of blood through stenosed tapered narrow arteries, treating blood as a two-fluid model with the suspension of all the erythrocytes in the core region as Herschel-Bulkley fluid and the plasma in the peripheral layer as Newtonian fluid.
Abstract: A computational model is developed to analyze the unsteady flow of blood through stenosed tapered narrow arteries, treating blood as a two-fluid model with the suspension of all the erythrocytes in the core region as Herschel-Bulkley fluid and the plasma in the peripheral layer as Newtonian fluid. The finite difference method is employed to solve the resulting system of nonlinear partial differential equations. The effects of stenosis height, peripheral layer thickness, yield stress, viscosity ratio, angle of tapering and power law index on the velocity, wall shear stress, flow rate and the longitudinal impedance are analyzed. It is found that the velocity and flow rate increase with the increase of the peripheral layer thickness and decrease with the increase of the angle of tapering and depth of the stenosis. It is observed that the flow rate decreases nonlinearly with the increase of the viscosity ratio and yield stress. The estimates of the increase in the longitudinal impedance to flow are considerably lower for the two-fluid Herschel-Bulkley model compared with those of the single-fluid Herschel-Bulkley model. Hence, it is concluded that the presence of the peripheral layer helps in the functioning of the diseased arterial system.
TL;DR: In this article, the Cauchy problem for a modified Helmholtz equation is considered and a spectral method together with the choice of regularization parameter is presented and error estimate is obtained.
Abstract: We consider the Cauchy problem for a modified Helmholtz equation, where the Cauchy data is given at and the solution is sought in the interval . A spectral method together with choice of regularization parameter is presented and error estimate is obtained. Combining the method of lines, we formulate regularized solutions which are stably convergent to the exact solutions.
TL;DR: By employing upper and lower solutions method together with maximal principle, the authors established a necessary and sufficient condition for the existence of pseudo- and positive solutions for fourth-order singular -Laplacian differential equations with integral boundary conditions.
Abstract: By employing upper and lower solutions method together with maximal principle, we establish a necessary and sufficient condition for the existence of pseudo-
as well as positive solutions for fourth-order singular -Laplacian differential equations with integral boundary conditions. Our nonlinearity may be singular at , , and . The dual results for the other integral boundary condition are also given.
TL;DR: In this article, the authors used a fixed point theorem in cones to investigate the multiple positive solutions of a boundary value problem for second-order singular differential equations on the half-line.
Abstract: This paper uses a fixed point theorem in cones to investigate the multiple positive solutions of a boundary value problem for second-order impulsive singular differential equations on the half-line. The conditions for the existence of multiple positive solutions are established.
TL;DR: In this article, the existence of periodic solutions of the second-order equation where is a Caratheodory function was studied by combining a new expression of Green's function together with Dancer's global bifurcation theorem.
Abstract: This paper is devoted to study the existence of periodic solutions of the second-order equation , where is a Caratheodory function, by combining a new expression of Green's function together with Dancer's global bifurcation theorem. Our main results are sharp and improve the main results by Torres (2003).
TL;DR: In this paper, the existence and energy decay of solution to the initial boundary value problem for the coupled Klein-Gordon-Schrodinger equations with acoustic boundary conditions was studied. But the existence of the solution was not investigated.
Abstract: We are concerned with the existence and energy decay of solution to the initial boundary value problem for the coupled Klein-Gordon-Schrodinger equations with acoustic boundary conditions.
TL;DR: In this paper, the authors demonstrate the existence of a unique weak solution to the infinite dimensional Trojan Y Chromosome system and obtain improved estimates on the upper bounds for the Hausdorff and fractal dimensions of the global attractor of the TYC system, via the use of weighted Sobolev spaces.
Abstract: The Trojan Y Chromosome strategy (TYC) is a theoretical method for eradication of invasive species. It requires constant introduction of artificial individuals into a target population, causing a shift in the sex ratio that ultimately leads to local extinction. In this work we demonstrate the existence of a unique weak solution to the infinite dimensional TYC system. Furthermore, we obtain improved estimates on the upper bounds for the Hausdorff and fractal dimensions of the global attractor of the TYC system, via the use of weighted Sobolev spaces. These results confirm that the TYC eradication strategy is a sound theoretical method of eradication of invasive species in a spatial setting. It also provides a solid ground for experiments in silico and validates the use of the TYC strategy in vivo.
TL;DR: In this paper, a general third-order nonlinear boundary value problem is considered, and an iterative algorithm with global convergence is presented, where the higher order derivatives of approximate solution can approximate the corresponding derivatives of exact solution well.
Abstract: We are concerned with general third-order nonlinear boundary value problems. An existence theorem of solution is given under weaker conditions. In the meantime, an iterative algorithm with global convergence is presented. The higher order derivatives of approximate solution is obtained by using this method can approximate the corresponding derivatives of exact solution well.