In this paper, we first obtain the existence of solution to some n-point boundary value problem for third-order differential equations using upper and lower solutions method. Based on the results, we explore singular ...In this paper, we first obtain the existence of solution to some n-point boundary value problem for third-order differential equations using upper and lower solutions method. Based on the results, we explore singular perturbation of another n-point boundary value problem for third-order differential equations with a small positive parameter. Finally, a uniformly valid asymptotic solution is constructed and the error estimation is given.展开更多
In this paper, we investigate a third-order differential equation. Based on the averaging theory, we obtain sufficient conditions for the existence of periodic solutions to the equation.
In this paper,we consider an abstract third-order differential equation and deduce some results on the maximal regularity of its strict solution.We assume that the inhomogeneity appearing in the right-hand term of thi...In this paper,we consider an abstract third-order differential equation and deduce some results on the maximal regularity of its strict solution.We assume that the inhomogeneity appearing in the right-hand term of this equation belongs to some anistropic Holder spaces.We illustrate our results by a BVP involving a 3D Laplacian posed in a cusp domain of R^(4).展开更多
We propose a new method for numerical solution of the third-order differential equations.The key idea is to use relaxation approximation to transform the nonlinear third-order differential equation to a semilinear sec...We propose a new method for numerical solution of the third-order differential equations.The key idea is to use relaxation approximation to transform the nonlinear third-order differential equation to a semilinear second-order differential system with a source term and a relaxation parameter.The relaxation system has linear characteristic variables and can be numerically solved without relying on Riemann problem solvers or linear iterations.A non-oscillatory finite volume method for the relaxation system is developed.The method is uniformly accurate for all relaxation rates.Numerical results are shown for some nonlinear problems such as the Korteweg-de Vires equation.Our method demonstrated the capability of accurately capturing soliton wave phenomena.展开更多
基金the Natural Science Foundation of Fujian Province (S0650010)Fujian Provincial Department of Sci.& Tech.(2005K028)Department of Education of FuJian Province (JB06098)
文摘In this paper, we first obtain the existence of solution to some n-point boundary value problem for third-order differential equations using upper and lower solutions method. Based on the results, we explore singular perturbation of another n-point boundary value problem for third-order differential equations with a small positive parameter. Finally, a uniformly valid asymptotic solution is constructed and the error estimation is given.
文摘In this paper, we investigate a third-order differential equation. Based on the averaging theory, we obtain sufficient conditions for the existence of periodic solutions to the equation.
文摘In this paper,we consider an abstract third-order differential equation and deduce some results on the maximal regularity of its strict solution.We assume that the inhomogeneity appearing in the right-hand term of this equation belongs to some anistropic Holder spaces.We illustrate our results by a BVP involving a 3D Laplacian posed in a cusp domain of R^(4).
文摘We propose a new method for numerical solution of the third-order differential equations.The key idea is to use relaxation approximation to transform the nonlinear third-order differential equation to a semilinear second-order differential system with a source term and a relaxation parameter.The relaxation system has linear characteristic variables and can be numerically solved without relying on Riemann problem solvers or linear iterations.A non-oscillatory finite volume method for the relaxation system is developed.The method is uniformly accurate for all relaxation rates.Numerical results are shown for some nonlinear problems such as the Korteweg-de Vires equation.Our method demonstrated the capability of accurately capturing soliton wave phenomena.
