In this paper, the existence of solutions for discontinuous nonlinear parabolic differential IBVP is proved by using a more generalized monotone iterative method. Moreover, the convergence of this method is discussed.
In this paper we investigate a model of one-dimensional isentropic bipolar hydrodynamical on the quarter plane,which takes the form of Euler-Poisson with electric field and frictional damping added to the momentum equ...In this paper we investigate a model of one-dimensional isentropic bipolar hydrodynamical on the quarter plane,which takes the form of Euler-Poisson with electric field and frictional damping added to the momentum equation.By using the classical energy method,we will prove the existence of classical solutions.展开更多
The main purpose of this paper is to consider the initial-boundary value problem for the 1D mixed nonlinear Schrodinger equation ut=iαu_(xx)+βu^(2)u_(x)+γ|u|^(2)u_(x)+i|u|^(2)u on the half-line with inhomogeneous b...The main purpose of this paper is to consider the initial-boundary value problem for the 1D mixed nonlinear Schrodinger equation ut=iαu_(xx)+βu^(2)u_(x)+γ|u|^(2)u_(x)+i|u|^(2)u on the half-line with inhomogeneous boundary condition.We combine Laplace transform method with restricted norm method to prove the local well-posedness and continuous dependence on initial and boundary data in low regularity Sobolev spaces.Moreover,we show that the nonlinear part of the solution on the half-line is smoother than the initial data.展开更多
We briefly introduce the applications of the inverse scattering method to some particular class of problems,which yield the exact solution or long time asymptotics in terms of the unique solution of a matrix Riemann-H...We briefly introduce the applications of the inverse scattering method to some particular class of problems,which yield the exact solution or long time asymptotics in terms of the unique solution of a matrix Riemann-Hilbert problem formulated in the complex plane.展开更多
文摘In this paper, the existence of solutions for discontinuous nonlinear parabolic differential IBVP is proved by using a more generalized monotone iterative method. Moreover, the convergence of this method is discussed.
文摘In this paper we investigate a model of one-dimensional isentropic bipolar hydrodynamical on the quarter plane,which takes the form of Euler-Poisson with electric field and frictional damping added to the momentum equation.By using the classical energy method,we will prove the existence of classical solutions.
文摘The main purpose of this paper is to consider the initial-boundary value problem for the 1D mixed nonlinear Schrodinger equation ut=iαu_(xx)+βu^(2)u_(x)+γ|u|^(2)u_(x)+i|u|^(2)u on the half-line with inhomogeneous boundary condition.We combine Laplace transform method with restricted norm method to prove the local well-posedness and continuous dependence on initial and boundary data in low regularity Sobolev spaces.Moreover,we show that the nonlinear part of the solution on the half-line is smoother than the initial data.
文摘We briefly introduce the applications of the inverse scattering method to some particular class of problems,which yield the exact solution or long time asymptotics in terms of the unique solution of a matrix Riemann-Hilbert problem formulated in the complex plane.
