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 authors consider the existence and uniqueness of the solution to the initial boundary value problem for a class of modified Zakharov equations, prove the global existence of the solution to the probl...In this paper the authors consider the existence and uniqueness of the solution to the initial boundary value problem for a class of modified Zakharov equations, prove the global existence of the solution to the problem by a priori integral estimates and Galerkin method.展开更多
A high-precision and space-time fully decoupled numerical method is developed for a class of nonlinear initial boundary value problems. It is established based on a proposed Coiflet-based approximation scheme with an ...A high-precision and space-time fully decoupled numerical method is developed for a class of nonlinear initial boundary value problems. It is established based on a proposed Coiflet-based approximation scheme with an adjustable high order for the functions over a bounded interval, which allows the expansion coefficients to be explicitly expressed by the function values at a series of single points. When the solution method is used, the nonlinear initial boundary value problems are first spatially discretized into a series of nonlinear initial value problems by combining the proposed wavelet approximation and the conventional Galerkin method, and a novel high-order step-by-step time integrating approach is then developed for the resulting nonlinear initial value problems with the same function approximation scheme based on the wavelet theory. The solution method is shown to have the N th-order accuracy, as long as the Coiflet with [0, 3 N-1]compact support is adopted, where N can be any positive even number. Typical examples in mechanics are considered to justify the accuracy and efficiency of the method.展开更多
A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems i...A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems is studied.展开更多
In this paper, we study the asymptotic behavior of the solutions to the initial boundary value problem for unipolar drift diffusion equations for semiconductors. Under the proper assumptions on doping profile and init...In this paper, we study the asymptotic behavior of the solutions to the initial boundary value problem for unipolar drift diffusion equations for semiconductors. Under the proper assumptions on doping profile and initial value, we prove that the smooth solutions to these evolutionary problems tend to the unique stationary solution exponentially as time tends to infinity.展开更多
In this paper,we apply Fokas unified method to study the initial boundary value(IBV)problems for nonlinear integrable equation with 3×3 Lax pair on the finite interval[0,L].The solution can be expressed by the so...In this paper,we apply Fokas unified method to study the initial boundary value(IBV)problems for nonlinear integrable equation with 3×3 Lax pair on the finite interval[0,L].The solution can be expressed by the solution of a 3×3 Riemann-Hilbert(RH)problem.The relevant jump matrices are written in terms of matrix-value spectral functions s(k),S(k),S_(l)(k),which are determined by initial data at t=0,boundary values at x=0 and boundary values at x=L,respectively.What's more,since the eigenvalues of 3×3 coefficient matrix of k spectral parameter in Lax pair are three different values,search for the path of analytic functions in RH problem becomes a very interesting thing.展开更多
Any classical non-null solution to the initial boundary value problem of Camassa-Holm equation on finite interval with homogeneous boundary condition must blow up in finite time. An initial boundary value problem of C...Any classical non-null solution to the initial boundary value problem of Camassa-Holm equation on finite interval with homogeneous boundary condition must blow up in finite time. An initial boundary value problem of CamassaHolm equation on half axis is also investigated in this paper. When the initial potential is nonnegative,then the classical solution exists globally; if the derivative of initial data on zero point is nonpositire, then the life span of nonzero solution nmst be finite.展开更多
In this paper,the existence,the uniqueness,the asymptotic behavior and the non-existence of the global generalized solutions of the initial boundary value problems for the non-linear pseudo-parabolic equation ut-αuxx...In this paper,the existence,the uniqueness,the asymptotic behavior and the non-existence of the global generalized solutions of the initial boundary value problems for the non-linear pseudo-parabolic equation ut-αuxx-βuxxt=F（u）-βF （u）xx are proved,where α,β 0 are constants,F（s） is a given function.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
The paper deal with the asymptotic behavior of the solutions to the initial boundary value problem for unipolar drift diffusion equations for semiconductors. Under the proper assumptions on doping profile and initial ...The paper deal with the asymptotic behavior of the solutions to the initial boundary value problem for unipolar drift diffusion equations for semiconductors. Under the proper assumptions on doping profile and initial value, we prove that the smooth solutions to these evolutionary problems tend to the unique stationary solution exponentially as time tends to infinity.展开更多
The singularly perturbed nonlinear noniocal initial boundary value problem for reaction diffusion equations is discussed. Under suitable conditions, the outer solution of the original problem is obtained. By using the...The singularly perturbed nonlinear noniocal initial boundary value problem for reaction diffusion equations is discussed. Under suitable conditions, the outer solution of the original problem is obtained. By using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed. By using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems are studied, and by educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are considered.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 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
In this paper,we study the Neumann boundary value problem of the Yang-Mills α-flow over a 4-dimensional compact Riemannian manifold with boundary.We establish the short-time existence of the Yang-Millsα-flow in the ...In this paper,we study the Neumann boundary value problem of the Yang-Mills α-flow over a 4-dimensional compact Riemannian manifold with boundary.We establish the short-time existence of the Yang-Millsα-flow in the framework of functional analysis and derive long-time existence and convergence results of classical solutions to the Yang-Millsα-flow,provided that theα-energy of initial connection is below some threshold.We also prove the validity of the boundary version of small energy estimates,removal of isolated singularities,and energy lower bound result for non-flat Yang-Mills connections.These results lead to the bubbling convergence of a sequence of Yang-Millsα-connections,and as an application,we demonstrate the existence of non-trivial Yang-Mills connections with Neumann boundary.展开更多
In this paper the singularly perturbed initial boundary value problems for the nonlocal reaction diffusion system are considered. Using the iteration method and the comparison theorem, the existence and its asymptotic...In this paper the singularly perturbed initial boundary value problems for the nonlocal reaction diffusion system are considered. Using the iteration method and the comparison theorem, the existence and its asymptotic behavior of the solution for the problem are studied.展开更多
In this paper we prove Phragmen-Lindelof type alternative.for foe initial boundaryproblem of Stokes equation, i. e. we show that the energy expression for the solutionof the initial boundary problem must either grow e...In this paper we prove Phragmen-Lindelof type alternative.for foe initial boundaryproblem of Stokes equation, i. e. we show that the energy expression for the solutionof the initial boundary problem must either grow exponentially or decay exponentiallywilh axial distance from the end of a semi-infinite strip. For the case of decay, we alsoestablish the pointwise estimate for the maximum module of the Stokes .flow andpresent a method for obtaining explicit bounds for the total energy.展开更多
In this paper we study an initial boundary value problem for a generalized complex Ginzburg-Landau equation with two spatial variables （2D）. Applying the notion of the ε-regular map we show the unique existence of ...In this paper we study an initial boundary value problem for a generalized complex Ginzburg-Landau equation with two spatial variables （2D）. Applying the notion of the ε-regular map we show the unique existence of global solutions for initial data with low regularity and the existence of the global attractor.展开更多
In this article we study the global existence of solutions to an initial boundary value problem for the Mullins equation which describes the groove development at the grain boundaries of a heated polycrystal, both the...In this article we study the global existence of solutions to an initial boundary value problem for the Mullins equation which describes the groove development at the grain boundaries of a heated polycrystal, both the Dirichlet and the Neumann boundary conditions are considered. For the classical solution we also investigate the large time behavior, it is proved that the solution converges to a constant, in the L^∞（Ω）-norm, as time tends to infinity.展开更多
This paper studies the initial boundary problems for semilinear strictly hyperbolic second-order equations with discontinuous data. Under the uniform Lopatinski boundary condition, the local existence theorem of disco...This paper studies the initial boundary problems for semilinear strictly hyperbolic second-order equations with discontinuous data. Under the uniform Lopatinski boundary condition, the local existence theorem of discontinuous solutions and the structure of singularities of the solutions are obtained.展开更多
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.
基金A Project Supported by Scientific Research Fund of Hunan Provincial Education Department (10C1056)Scientific Research Found of Huaihua University (HHUY2011-01)
文摘In this paper the authors consider the existence and uniqueness of the solution to the initial boundary value problem for a class of modified Zakharov equations, prove the global existence of the solution to the problem by a priori integral estimates and Galerkin method.
基金Project supported by the National Natural Science Foundation of China(No.11472119)the Fundamental Research Funds for the Central Universities(No.lzujbky-2017-ot11)the 111 Project(No.B14044)
文摘A high-precision and space-time fully decoupled numerical method is developed for a class of nonlinear initial boundary value problems. It is established based on a proposed Coiflet-based approximation scheme with an adjustable high order for the functions over a bounded interval, which allows the expansion coefficients to be explicitly expressed by the function values at a series of single points. When the solution method is used, the nonlinear initial boundary value problems are first spatially discretized into a series of nonlinear initial value problems by combining the proposed wavelet approximation and the conventional Galerkin method, and a novel high-order step-by-step time integrating approach is then developed for the resulting nonlinear initial value problems with the same function approximation scheme based on the wavelet theory. The solution method is shown to have the N th-order accuracy, as long as the Coiflet with [0, 3 N-1]compact support is adopted, where N can be any positive even number. Typical examples in mechanics are considered to justify the accuracy and efficiency of the method.
文摘A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems is studied.
文摘In this paper, we study the asymptotic behavior of the solutions to the initial boundary value problem for unipolar drift diffusion equations for semiconductors. Under the proper assumptions on doping profile and initial value, we prove that the smooth solutions to these evolutionary problems tend to the unique stationary solution exponentially as time tends to infinity.
基金supported by the National Natural Science Foundation of China(11901167,11971313 and 51879045)Key scientific research projects of higher education institutions in Henan,China(18B110008).
文摘In this paper,we apply Fokas unified method to study the initial boundary value(IBV)problems for nonlinear integrable equation with 3×3 Lax pair on the finite interval[0,L].The solution can be expressed by the solution of a 3×3 Riemann-Hilbert(RH)problem.The relevant jump matrices are written in terms of matrix-value spectral functions s(k),S(k),S_(l)(k),which are determined by initial data at t=0,boundary values at x=0 and boundary values at x=L,respectively.What's more,since the eigenvalues of 3×3 coefficient matrix of k spectral parameter in Lax pair are three different values,search for the path of analytic functions in RH problem becomes a very interesting thing.
基金Supported by the National Natural Science Founda-tion of China (10131050)
文摘Any classical non-null solution to the initial boundary value problem of Camassa-Holm equation on finite interval with homogeneous boundary condition must blow up in finite time. An initial boundary value problem of CamassaHolm equation on half axis is also investigated in this paper. When the initial potential is nonnegative,then the classical solution exists globally; if the derivative of initial data on zero point is nonpositire, then the life span of nonzero solution nmst be finite.
基金Supported by the National Natural Science Foundation of China（10671182）
文摘In this paper,the existence,the uniqueness,the asymptotic behavior and the non-existence of the global generalized solutions of the initial boundary value problems for the non-linear pseudo-parabolic equation ut-αuxx-βuxxt=F（u）-βF （u）xx are proved,where α,β 0 are constants,F（s） is a given function.
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.
文摘The paper deal with the asymptotic behavior of the solutions to the initial boundary value problem for unipolar drift diffusion equations for semiconductors. Under the proper assumptions on doping profile and initial value, we prove that the smooth solutions to these evolutionary problems tend to the unique stationary solution exponentially as time tends to infinity.
基金The NNSF (90111011 and 10471039) of Chinathe National Key Project for Basics Research (2003CB415101-03 and 2004CB418304)the Key Project of the Chinese Academy of Sciences (KZCX3-SW-221)in part by E-Institutes of Shanghai Municipal Education Commission (N.E03004)
文摘The singularly perturbed nonlinear noniocal initial boundary value problem for reaction diffusion equations is discussed. Under suitable conditions, the outer solution of the original problem is obtained. By using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed. By using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems are studied, and by educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are considered.
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 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supported by the National Natural Science Foundation of China(12201515)the National Natural Science Foundation of China(12171314)+1 种基金partially supported by the Innovation Program of Shanghai Municipal Education Commission(2021-01-07-00-02-E00087)the Shanghai Frontier Science Center of Modern Analysis。
文摘In this paper,we study the Neumann boundary value problem of the Yang-Mills α-flow over a 4-dimensional compact Riemannian manifold with boundary.We establish the short-time existence of the Yang-Millsα-flow in the framework of functional analysis and derive long-time existence and convergence results of classical solutions to the Yang-Millsα-flow,provided that theα-energy of initial connection is below some threshold.We also prove the validity of the boundary version of small energy estimates,removal of isolated singularities,and energy lower bound result for non-flat Yang-Mills connections.These results lead to the bubbling convergence of a sequence of Yang-Millsα-connections,and as an application,we demonstrate the existence of non-trivial Yang-Mills connections with Neumann boundary.
基金Supported by the National Natural Science Foundation of China(No.90111011,No.10471039)the National Key Project for Basics Research(2003CB415101-03 and 2004CB418304)+1 种基金the Key Project of the Chinese Academy of Sciences(KZCX3-SW-221)in part by E-Insitutes of Shanghai Municipal Education Commission(N.E03004).
文摘In this paper the singularly perturbed initial boundary value problems for the nonlocal reaction diffusion system are considered. Using the iteration method and the comparison theorem, the existence and its asymptotic behavior of the solution for the problem are studied.
文摘In this paper we prove Phragmen-Lindelof type alternative.for foe initial boundaryproblem of Stokes equation, i. e. we show that the energy expression for the solutionof the initial boundary problem must either grow exponentially or decay exponentiallywilh axial distance from the end of a semi-infinite strip. For the case of decay, we alsoestablish the pointwise estimate for the maximum module of the Stokes .flow andpresent a method for obtaining explicit bounds for the total energy.
基金This work is supported by National Natural Science Foundation of China under Grant nos, 10001013 and 10471047 and Natural Science Foundation of Guangdong Province of China under Grant no. 004020077.
文摘In this paper we study an initial boundary value problem for a generalized complex Ginzburg-Landau equation with two spatial variables （2D）. Applying the notion of the ε-regular map we show the unique existence of global solutions for initial data with low regularity and the existence of the global attractor.
文摘In this article we study the global existence of solutions to an initial boundary value problem for the Mullins equation which describes the groove development at the grain boundaries of a heated polycrystal, both the Dirichlet and the Neumann boundary conditions are considered. For the classical solution we also investigate the large time behavior, it is proved that the solution converges to a constant, in the L^∞（Ω）-norm, as time tends to infinity.
基金Research supported by the Natural Science Foundation of Fujian Province, China.
文摘This paper studies the initial boundary problems for semilinear strictly hyperbolic second-order equations with discontinuous data. Under the uniform Lopatinski boundary condition, the local existence theorem of discontinuous solutions and the structure of singularities of the solutions are obtained.
