Positive solutions of second-order differential systems with nonhomogeneous boundary conditions

This paper is to investigate the positive solutions of the systems of second-order ordinary differential equations with nonhomogeneous multi-point boundary conditions. By the lower and upper solutions method, Schauder fixed point theorem and fixed point index theory, under certain conditions, it is proved that there exist appropriate regions of parameters in which the problem has at least two, at least one or no positive solution.

Dynamic stability of axially accelerating viscoelastic plates with longitudinally varying tensions

The dynamic stability of axially accelerating plates is investigated. Longitudi- nally varying tensions due to the acceleration and nonhomogeneous boundary conditions are highlighted. A model of the plate combined with viscoelasticity is applied. In the viscoelastic constitutive relationship, the material derivative is used to take the place of the partial time derivative. Analytical and numerical methods are used to investigate summation and principal parametric resonances, respectively. By use of linear models for the transverse behavior in the small displacement regime, the plate is confined by a viscous damping force. The generalized Hamilton principle is used to derive the govern- ing equations, the initial conditions, and the boundary conditions of the coupled planar vibration. The solvability conditions are established by directly using the method of mul- tiple scales. The Routh-Hurwitz criterion is used to obtain the necessary and sufficient condition of the stability. Numerical examples are given to show the effects of related parameters on the stability boundaries. The validity of longitudinally varying tensions and nonhomogeneous boundary conditions is highlighted by comparing the results of the method of multiple scales with those of a differential quadrature scheme.

The Initial Boundary Value Problem for Navier-Stokes Equations

By making full use of the estimates of solutions to nonstationary Stokes equations and the method discussing global stability, we establish the global existence theorem of strong solutions for Navier-Stokes equations in arbitrary three dimensional domain with uniformly C3 boundary, under the assumption that ‖a‖L^2(Ω)+‖f‖L^1(o,∞;L^2(Ω)) or‖▽a‖L^2(Ω)+‖f‖L^2(o,∞;L^2(Ω)) small or viscosity, large. Here a is a given initial velocity and f is the external force. This improves on the previous results. Moreover, the solvability of the case with nonhomogeneous boundary conditions is also discussed.

Oseen Coupling Method for the Exterior Flow Part Ⅰ:Oseen Coupling Approximation

In this paper, we consider the bidimensional exterior unsteady Navier-Stokes equations with nonhomogeneous boundary conditions and present an Oseen coupling problem which approximates the Navier-Stokes problem, obtained by coupling the Navier-Stokes equations in the inner region and the Oseen equations in the outer region. Moreover, we prove the existence, uniqueness and the approximate accuracy of the weak solution of the Oseen coupling equations.

A Discontinuous Galerkin Finite Element Method without Interior Penalty Terms

A conforming discontinuous Galerkinfinite element method was introduced by Ye and Zhang,on simplicial meshes and on polytopal meshes,which has theflexibility of using discontinuous approximation and an ultra simple formulation.The main goal of this paper is to improve the above discontinuous Galerkinfinite element method so that it can handle nonhomogeneous Dirichlet boundary conditions effectively.In addition,the method has been generalized in terms of approximation of the weak gradient.Error estimates of optimal order are established for the correspond-ing discontinuousfinite element approximation in both a discrete H1 norm and the L2 norm.Numerical results are presented to confirm the theory.