In this paper we make a study of the use of the iniiai values of a recursion skilfully, so that the count for finding a solution of any recursion will be more simplified. Finally, we give out the "moving forth pr...In this paper we make a study of the use of the iniiai values of a recursion skilfully, so that the count for finding a solution of any recursion will be more simplified. Finally, we give out the "moving forth prineiple" of initial values of a recursion.展开更多
In this paper, we consider a strongly-coupled parabolic system with initial boundary values. Under the appropriate conditions, using Gagliard-Nirenberg inequality, Poincare inequality, Gronwall inequality and imbeddin...In this paper, we consider a strongly-coupled parabolic system with initial boundary values. Under the appropriate conditions, using Gagliard-Nirenberg inequality, Poincare inequality, Gronwall inequality and imbedding theorem, we obtain the global existence of solutions.展开更多
The nonlinear interactions between the monochromatic wave have been considered by K. Matsunchi, who also proposed one class of the nonlinear Schrdinger equation system with wave operator. We also obtain the same type ...The nonlinear interactions between the monochromatic wave have been considered by K. Matsunchi, who also proposed one class of the nonlinear Schrdinger equation system with wave operator. We also obtain the same type of equations, which are satisfied by transverse velocity of higher frequency electron, as we study soliton in plasma physics. In this paper, under some condition we study the existence and nonexistence for this equations in the cases possessing different signs in nonlinear term.展开更多
In this paper, the mixed initial-boundary value problem for general first order quasi- linear hyperbolic systems with nonlinear boundary conditions in the domain D = {（t, x） ｜ t ≥ 0, x ≥0} is considered. A suffic...In this paper, the mixed initial-boundary value problem for general first order quasi- linear hyperbolic systems with nonlinear boundary conditions in the domain D = {（t, x） ｜ t ≥ 0, x ≥0} is considered. A sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution is given.展开更多
In this paper, the global existence of weak s olutions to the initial boundary value problem for Boltzmann-Poisson system is proved. The proof is based on the regularization and the stability of the veloci ty averages...In this paper, the global existence of weak s olutions to the initial boundary value problem for Boltzmann-Poisson system is proved. The proof is based on the regularization and the stability of the veloci ty averages and the compactness results on L 1-theory.展开更多
This paper deals with the initial boundary value problem for the Boltzmann-Poisson system, which arises in semiconductor physics, with absorbing boundary. The global existence of weak solutions is proved by using the ...This paper deals with the initial boundary value problem for the Boltzmann-Poisson system, which arises in semiconductor physics, with absorbing boundary. The global existence of weak solutions is proved by using the stability of velocity averages and the compactness results on L1-theory under weaker conditons on initial boundary values.展开更多
In this paper, the existence and uniqueness of the local generalized solution of the initial boundary value problem for a nonlinear hyperbolic equation are proved by the contraction mapping principle and the sufficien...In this paper, the existence and uniqueness of the local generalized solution of the initial boundary value problem for a nonlinear hyperbolic equation are proved by the contraction mapping principle and the sufficient conditions of blow_up of the solution in finite time are given.展开更多
We present the optimal homotopy asymptotic method (OHAM) to find the numerical solution of the second order initial value problems of Bratu-type. We solve some examples to illustrate the validity and efficiency of the...We present the optimal homotopy asymptotic method (OHAM) to find the numerical solution of the second order initial value problems of Bratu-type. We solve some examples to illustrate the validity and efficiency of the method.展开更多
This paper is concerned with the initial-boundary value problem of scalar conservation laws with weak discontinuous flux, whose initial data are a function with two pieces of constant and whose boundary data are a con...This paper is concerned with the initial-boundary value problem of scalar conservation laws with weak discontinuous flux, whose initial data are a function with two pieces of constant and whose boundary data are a constant function. Under the condition that the flux function has a finite number of weak discontinuous points, by using the structure of weak entropy solution of the corresponding initial value problem and the boundary entropy condition developed by Bardos-Leroux-Nedelec, we give a construction method to the global weak entropy solution for this initial-boundary value problem, and by investigating the interaction of elementary waves and the boundary, we clarify the geometric structure and the behavior of boundary for the weak entropy solution.展开更多
This paper studies the initial boundary value problem for a generalized Boussinese equation and proves the existence and uniqueness of the local generalized solution of the problem by using the Galerkin method. Moreov...This paper studies the initial boundary value problem for a generalized Boussinese equation and proves the existence and uniqueness of the local generalized solution of the problem by using the Galerkin method. Moreover, it gives the sufficient conditions of blow-up of the solution in finite time by using the concavity method.展开更多
In this paper, two kinds of initial boundary value problems for Kuramoto_Sivashinsky equation are considered. Some prior estimates are derived by Galerkin methods. The existence, uniqueness and regularities of the gen...In this paper, two kinds of initial boundary value problems for Kuramoto_Sivashinsky equation are considered. Some prior estimates are derived by Galerkin methods. The existence, uniqueness and regularities of the generalized global solutions and the classical global solutions for the equation are proved. Morever, the asymptotic behavior of these solutions are considered under some conditions.展开更多
In this paper,the asymptotics of the solution of the initial boundary value problem for a sixth-order nonlinear partial differential equation of Boussinesq type is studied.First,the energy function is obtained.Then,ap...In this paper,the asymptotics of the solution of the initial boundary value problem for a sixth-order nonlinear partial differential equation of Boussinesq type is studied.First,the energy function is obtained.Then,apriori evaluations for this function are obtained.Then,by imposing some conditions on the function on the right-hand side of the equation and using appropriate inequalities,it is shown that the solution is asymptotically damped.展开更多
The initial value problem for the quantum Zakharov equation in three di- mensions is studied. The existence and uniqueness of a global smooth solution are proven with coupled a priori estimates and the Galerkin method.
In this paper, a new set of sufficient conditions related to an initial value problem and global homeomorphism is obtained in discussing the existence and uniqueness of 2π-periodic solution for 2kth order differentia...In this paper, a new set of sufficient conditions related to an initial value problem and global homeomorphism is obtained in discussing the existence and uniqueness of 2π-periodic solution for 2kth order differential equations with resonance. The key role is played by nonnegative auxiliary scalar coercive function. The result of this paper generalizes some existed theorems.展开更多
This paper studies the conditions of blow up in finite time of solutions of initial boundary value problem for a class nonlinear doubly degenerate parabolic equation.
The approximate generalized conditional symmetries of nonlinear filtration equation with a small parameter are studied. The initial-value problem of the equation can be transformed to perturbed Cauchy problem of pertu...The approximate generalized conditional symmetries of nonlinear filtration equation with a small parameter are studied. The initial-value problem of the equation can be transformed to perturbed Cauchy problem of perturbed first-order ordinary dif- ferential equations systems and approximate solutions are obtained by using these symmetries.展开更多
Concerns with the nonexistence of global solutions to the initial boundary value problem for a nonlinear hyperbolic equation with material damping. Nonexitence theorems of global solutions to the above problem are pro...Concerns with the nonexistence of global solutions to the initial boundary value problem for a nonlinear hyperbolic equation with material damping. Nonexitence theorems of global solutions to the above problem are proved by the energy method, Jensen inequality and the concavity method, respectively. As applications of our main results, three examples are given.展开更多
In the present paper we investigate existence and uniqueness generalized solution for initial boundary value problem of synoptic flow equation with discontinuous boundary conditions. We consider Rothe-Galerkin method ...In the present paper we investigate existence and uniqueness generalized solution for initial boundary value problem of synoptic flow equation with discontinuous boundary conditions. We consider Rothe-Galerkin method for given problem and reduce numerical calculations.展开更多
In this paper, we consider the initial value problem for a complete integrable equation introduced by Wadati-Konno-Ichikawa (WKI). The solution ?is reconstructed in terms of the solution of a ?matrix Riemann-Hilbert p...In this paper, we consider the initial value problem for a complete integrable equation introduced by Wadati-Konno-Ichikawa (WKI). The solution ?is reconstructed in terms of the solution of a ?matrix Riemann-Hilbert problem via the asymptotic behavior of the spectral variable at one non-singularity point, i.e., . Then, the one-cuspon solution, two-cuspon solutions and three-cuspon solution are discussed in detail. Further, the numerical simulations are given to show the dynamic behaviors of these soliton solutions.展开更多
This paper is concerned with the initial-boundary value problem of a nonlinear conservation law in the half space R+= {x |x > 0} where a>0 , u(x,t) is an unknown function of x ∈ R+ and t>0 , u ± , um ar...This paper is concerned with the initial-boundary value problem of a nonlinear conservation law in the half space R+= {x |x > 0} where a>0 , u(x,t) is an unknown function of x ∈ R+ and t>0 , u ± , um are three given constants satisfying um=u+≠u- or um=u-≠u+ , and the flux function f is a given continuous function with a weak discontinuous point ud. The main purpose of our present manuscript is devoted to studying the structure of the global weak entropy solution for the above initial-boundary value problem under the condition of f '-(ud) > f '+(ud). By the characteristic method and the truncation method, we construct the global weak entropy solution of this initial-boundary value problem, and investigate the interaction of elementary waves with the boundary and the boundary behavior of the weak entropy solution.展开更多
文摘In this paper we make a study of the use of the iniiai values of a recursion skilfully, so that the count for finding a solution of any recursion will be more simplified. Finally, we give out the "moving forth prineiple" of initial values of a recursion.
文摘In this paper, we consider a strongly-coupled parabolic system with initial boundary values. Under the appropriate conditions, using Gagliard-Nirenberg inequality, Poincare inequality, Gronwall inequality and imbedding theorem, we obtain the global existence of solutions.
文摘The nonlinear interactions between the monochromatic wave have been considered by K. Matsunchi, who also proposed one class of the nonlinear Schrdinger equation system with wave operator. We also obtain the same type of equations, which are satisfied by transverse velocity of higher frequency electron, as we study soliton in plasma physics. In this paper, under some condition we study the existence and nonexistence for this equations in the cases possessing different signs in nonlinear term.
文摘In this paper, the mixed initial-boundary value problem for general first order quasi- linear hyperbolic systems with nonlinear boundary conditions in the domain D = {（t, x） ｜ t ≥ 0, x ≥0} is considered. A sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution is given.
文摘In this paper, the global existence of weak s olutions to the initial boundary value problem for Boltzmann-Poisson system is proved. The proof is based on the regularization and the stability of the veloci ty averages and the compactness results on L 1-theory.
基金1. The NNSF (0111051400) of Henan Province2. The OYF (0016) of Henan Province.
文摘This paper deals with the initial boundary value problem for the Boltzmann-Poisson system, which arises in semiconductor physics, with absorbing boundary. The global existence of weak solutions is proved by using the stability of velocity averages and the compactness results on L1-theory under weaker conditons on initial boundary values.
文摘In this paper, the existence and uniqueness of the local generalized solution of the initial boundary value problem for a nonlinear hyperbolic equation are proved by the contraction mapping principle and the sufficient conditions of blow_up of the solution in finite time are given.
文摘We present the optimal homotopy asymptotic method (OHAM) to find the numerical solution of the second order initial value problems of Bratu-type. We solve some examples to illustrate the validity and efficiency of the method.
文摘This paper is concerned with the initial-boundary value problem of scalar conservation laws with weak discontinuous flux, whose initial data are a function with two pieces of constant and whose boundary data are a constant function. Under the condition that the flux function has a finite number of weak discontinuous points, by using the structure of weak entropy solution of the corresponding initial value problem and the boundary entropy condition developed by Bardos-Leroux-Nedelec, we give a construction method to the global weak entropy solution for this initial-boundary value problem, and by investigating the interaction of elementary waves and the boundary, we clarify the geometric structure and the behavior of boundary for the weak entropy solution.
基金Project supported by the National Natural Science Foundation of China (No.10671182)the Excellent Youth Teachers Foundation of High College of Henan Province of China
文摘This paper studies the initial boundary value problem for a generalized Boussinese equation and proves the existence and uniqueness of the local generalized solution of the problem by using the Galerkin method. Moreover, it gives the sufficient conditions of blow-up of the solution in finite time by using the concavity method.
文摘In this paper, two kinds of initial boundary value problems for Kuramoto_Sivashinsky equation are considered. Some prior estimates are derived by Galerkin methods. The existence, uniqueness and regularities of the generalized global solutions and the classical global solutions for the equation are proved. Morever, the asymptotic behavior of these solutions are considered under some conditions.
文摘In this paper,the asymptotics of the solution of the initial boundary value problem for a sixth-order nonlinear partial differential equation of Boussinesq type is studied.First,the energy function is obtained.Then,apriori evaluations for this function are obtained.Then,by imposing some conditions on the function on the right-hand side of the equation and using appropriate inequalities,it is shown that the solution is asymptotically damped.
基金Project supported by the National Natural Science Foundation of China(No.11501232)the Research Foundation of Education Bureau of Hunan Province(No.15B185)
文摘The initial value problem for the quantum Zakharov equation in three di- mensions is studied. The existence and uniqueness of a global smooth solution are proven with coupled a priori estimates and the Galerkin method.
基金Foundation item： Supported by the Natural Science Foundation of Changzhou Instituty of Technology（YN09090） Supported by the Natural Science Foundation of Jiangsu Province（13KJD110001）
文摘In this paper, a new set of sufficient conditions related to an initial value problem and global homeomorphism is obtained in discussing the existence and uniqueness of 2π-periodic solution for 2kth order differential equations with resonance. The key role is played by nonnegative auxiliary scalar coercive function. The result of this paper generalizes some existed theorems.
文摘This paper studies the conditions of blow up in finite time of solutions of initial boundary value problem for a class nonlinear doubly degenerate parabolic equation.
基金Supported by the National Natural Science Foundation of China(11326167,11226195)the Natural Science Foundation of Henan Province(142300410354)Foundation of Henan Educational Committee(13A110119,15B110012)
文摘The approximate generalized conditional symmetries of nonlinear filtration equation with a small parameter are studied. The initial-value problem of the equation can be transformed to perturbed Cauchy problem of perturbed first-order ordinary dif- ferential equations systems and approximate solutions are obtained by using these symmetries.
基金Project supported by the National Natural Science Foundation of China (Nos. 10371073 and 10572156) the Natural Science Foundation of Henan Province of China (No.0611050500)
文摘Concerns with the nonexistence of global solutions to the initial boundary value problem for a nonlinear hyperbolic equation with material damping. Nonexitence theorems of global solutions to the above problem are proved by the energy method, Jensen inequality and the concavity method, respectively. As applications of our main results, three examples are given.
文摘In the present paper we investigate existence and uniqueness generalized solution for initial boundary value problem of synoptic flow equation with discontinuous boundary conditions. We consider Rothe-Galerkin method for given problem and reduce numerical calculations.
文摘In this paper, we consider the initial value problem for a complete integrable equation introduced by Wadati-Konno-Ichikawa (WKI). The solution ?is reconstructed in terms of the solution of a ?matrix Riemann-Hilbert problem via the asymptotic behavior of the spectral variable at one non-singularity point, i.e., . Then, the one-cuspon solution, two-cuspon solutions and three-cuspon solution are discussed in detail. Further, the numerical simulations are given to show the dynamic behaviors of these soliton solutions.
文摘This paper is concerned with the initial-boundary value problem of a nonlinear conservation law in the half space R+= {x |x > 0} where a>0 , u(x,t) is an unknown function of x ∈ R+ and t>0 , u ± , um are three given constants satisfying um=u+≠u- or um=u-≠u+ , and the flux function f is a given continuous function with a weak discontinuous point ud. The main purpose of our present manuscript is devoted to studying the structure of the global weak entropy solution for the above initial-boundary value problem under the condition of f '-(ud) > f '+(ud). By the characteristic method and the truncation method, we construct the global weak entropy solution of this initial-boundary value problem, and investigate the interaction of elementary waves with the boundary and the boundary behavior of the weak entropy solution.
