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 propose a numerical calculation model of the multigroup neutron diffusion equation in 3D hexagonal geometry using the nodal Green's function method and verified it.We obtained one-dimensional tran...In this paper,we propose a numerical calculation model of the multigroup neutron diffusion equation in 3D hexagonal geometry using the nodal Green's function method and verified it.We obtained one-dimensional transverse integrated equations using the transverse integration procedure over 3D hexagonal geometry and denoted the solutions as a nodal Green's functions under the Neumann boundary condition.By applying a quadratic polynomial expansion of the transverse-averaged quantities,we derived the net neutron current coupling equation,equation for the expansion coefficients of the transverse-averaged neutron flux,and formulas for the coefficient matrix of these equations.We formulated the closed system of equations in correspondence with the boundary conditions.The proposed model was tested by comparing it with the benchmark for the VVER-440 reactor,and the numerical results were in good agreement with the reference solutions.展开更多
In this article, we consider a backward problem in time of the diffusion equation with local and nonlocal operators. This inverse problem is ill-posed because the solution does not depend continuously on the measured ...In this article, we consider a backward problem in time of the diffusion equation with local and nonlocal operators. This inverse problem is ill-posed because the solution does not depend continuously on the measured data. Inspired by the classical Landweber iterative method and Fourier truncation technique, we develops a modified Landweber iterative regularization method to restore the continuous dependence of solution on the measurement data. Under the a-priori and a-posteriori choice rules for the regularized parameter, the convergence estimates for the regularization method are derived. Some results of numerical simulation are provided to verify the stability and feasibility of our method in dealing with the considered problem.展开更多
A class of nonlinear for singularly perturbed problems for reaction diffusion equations with time delays are considered. Under suitable conditions, using theory of differential inequalities the asymptotic behavior of ...A class of nonlinear for singularly perturbed problems for reaction diffusion equations with time delays are considered. Under suitable conditions, using theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems are studied.展开更多
A class of nonlinear singularly perturbed problems for reaction diffusion equations are considered. Under suitable conditions, by using the theory of differential inequalities, the asymptotic behavior of solutions for...A class of nonlinear singularly perturbed problems for reaction diffusion equations are considered. Under suitable conditions, by using the theory of differential inequalities, the asymptotic behavior of solutions for the initial boundary value problems are studied, reduced problems of which possess two intersecting solutions.展开更多
In this article the travelling wave solution for a class of nonlinear reaction diffusion problems are considered. Using the homotopic method and the theory of travelling wave transform, the approximate solution for th...In this article the travelling wave solution for a class of nonlinear reaction diffusion problems are considered. Using the homotopic method and the theory of travelling wave transform, the approximate solution for the corresponding problem is obtained.展开更多
In this paper, a class of nonlinear singularly perturbed initial boundary value problems for reaction diffusion equations with boundary perturbation are considered under suitable conditions. Firstly, by dint of the re...In this paper, a class of nonlinear singularly perturbed initial boundary value problems for reaction diffusion equations with boundary perturbation are considered under suitable conditions. Firstly, by dint of the regular perturbation method, the outer solution of the original problem is obtained. Secondly, by using the stretched variable and the expansion theory of power series the initial layer of the solution is constructed. And then, by using the theory of differential inequalities, the asymptotic behavior of the solution for the initial boundary value problems is studied. Finally, using some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.展开更多
A class of differential-difference reaction diffusion equations with a small time delay is considered.Under suitable conditions and by using the method of the stretched variable,the formal asymptotic solution is const...A class of differential-difference reaction diffusion equations with a small time delay is considered.Under suitable conditions and by using the method of the stretched variable,the formal asymptotic solution is constructed.And then,by using the theory of differential inequalities the uniformly validity of solution is proved.展开更多
The nonlinear nonlocal singularly perturbed initial boundary value problems for reaction diffusion equations with a boundary perturbation is considered. Under suitable conditions, the outer solution of the original pr...The nonlinear nonlocal singularly perturbed initial boundary value problems for reaction diffusion equations with a boundary perturbation is considered. Under suitable conditions, the outer solution of the original problem is obtained. Using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed. And then using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems is studied. Finally the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.展开更多
The singular perturbation problem for reaction diffusion time delay equation with boundary perturbation is considered. Firstly, the outer solution for the initial boundary value problem is constructed. Then, the initi...The singular perturbation problem for reaction diffusion time delay equation with boundary perturbation is considered. Firstly, the outer solution for the initial boundary value problem is constructed. Then, the initial and boundary layer correction terms are obtained using the stretched variables transforms. Finally, the asymptotic behavior of solution for the initial boundary value problem is studied.展开更多
A class of singularly perturbed Robin problems for reaction diffusion equation is considered. Under suitable conditions the asymptotic behavior of the generalized solution for the problems are studied.
A class of nonlinear initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions and using the theory of differential inequalities the asymptoti...A class of nonlinear initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions and using the theory of differential inequalities the asymptotic solution of the initial boundary value problems is studied.展开更多
This paper studies the time asymptotic behavior of solutions for a nonlinear convection diffusion reaction equation in one dimension.First,the pointwise estimates of solutions are obtained,furthermore,we obtain the op...This paper studies the time asymptotic behavior of solutions for a nonlinear convection diffusion reaction equation in one dimension.First,the pointwise estimates of solutions are obtained,furthermore,we obtain the optimal Lp,1≤ p ≤ ＋∞,convergence rate of solutions for small initial data.Then we establish the local existence of solutions,the blow up criterion and the sufficient condition to ensure the nonnegativity of solutions for large initial data.Our approach is based on the detailed analysis of the Green function of the linearized equation and some energy estimates.展开更多
The singularly perturbed initial boundary value problems for reaction diffusion equations are considered.Under suitable conditions and by using the theory of differential inequality,the asymptotic behavior of solution...The singularly perturbed initial boundary value problems for reaction diffusion equations are considered.Under suitable conditions and by using the theory of differential inequality,the asymptotic behavior of solution for initial boundary value problems are studied,where the reduced problems possess two intersecting solutions.展开更多
A mathematical model of CE reaction schemes under first or pseudo-first order conditions with different diffusion coefficients at a spherical electrode under non-steady-state conditions is described. The model is base...A mathematical model of CE reaction schemes under first or pseudo-first order conditions with different diffusion coefficients at a spherical electrode under non-steady-state conditions is described. The model is based on non-stationary diffusion equation containing a non-linear reaction term. This paper presents the complex numerical method (Homotopy perturbation method) to solve the system of non-linear differential equation that describes the homogeneous processes coupled to electrode reaction. In this paper the approximate analytical expressions of the non-steady-state concentrations and current at spherical electrodes for homogeneous reactions mechanisms are derived for all values of the reaction diffusion parameters. These approximate results are compared with the available analytical results and are found to be in good agreement.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
The singularly perturbed initial boundary value problem for a class of reaction diffusion equation is considered. Under appropriate conditions, the existence-uniqueness and the asymptotic behavior of the solution are ...The singularly perturbed initial boundary value problem for a class of reaction diffusion equation is considered. Under appropriate conditions, the existence-uniqueness and the asymptotic behavior of the solution are showed by using the fixed-point theorem.展开更多
A class of initial boundary value problems of differential-difference equations for reaction diffusion with a small time delay is considered. Under suitable conditions and by using the stretched variable method, a for...A class of initial boundary value problems of differential-difference equations for reaction diffusion with a small time delay is considered. Under suitable conditions and by using the stretched variable method, a formal asymptotic solution is constructed. Then, by use of the theory of differential inequalities, the uniform validity of the solution is proved.展开更多
A class of nonlinear nonlocal for singularly perturbed Robin initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions, first, the outer solut...A class of nonlinear nonlocal for singularly perturbed Robin initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions, first, the outer solution of the original problem was obtained. Secondly, using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer was constructed. Finally, using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems was studied, and educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation were discussed.展开更多
In this paper,a class of slow reaction-diffusion equations with nonlocal source and inner absorption terms are studied.By using the technique of improved differential inequality,the lower bounds of blow up time for th...In this paper,a class of slow reaction-diffusion equations with nonlocal source and inner absorption terms are studied.By using the technique of improved differential inequality,the lower bounds of blow up time for the system under either homogeneous Dirichlet or nonhomogeneous Neumann boundary conditions are obtained.展开更多
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 propose a numerical calculation model of the multigroup neutron diffusion equation in 3D hexagonal geometry using the nodal Green's function method and verified it.We obtained one-dimensional transverse integrated equations using the transverse integration procedure over 3D hexagonal geometry and denoted the solutions as a nodal Green's functions under the Neumann boundary condition.By applying a quadratic polynomial expansion of the transverse-averaged quantities,we derived the net neutron current coupling equation,equation for the expansion coefficients of the transverse-averaged neutron flux,and formulas for the coefficient matrix of these equations.We formulated the closed system of equations in correspondence with the boundary conditions.The proposed model was tested by comparing it with the benchmark for the VVER-440 reactor,and the numerical results were in good agreement with the reference solutions.
基金supported by the NSF of Ningxia(2022AAC03234)the NSF of China(11761004),the Construction Project of First-Class Disciplines in Ningxia Higher Education(NXYLXK2017B09)the Postgraduate Innovation Project of North Minzu University(YCX23074).
文摘In this article, we consider a backward problem in time of the diffusion equation with local and nonlocal operators. This inverse problem is ill-posed because the solution does not depend continuously on the measured data. Inspired by the classical Landweber iterative method and Fourier truncation technique, we develops a modified Landweber iterative regularization method to restore the continuous dependence of solution on the measurement data. Under the a-priori and a-posteriori choice rules for the regularized parameter, the convergence estimates for the regularization method are derived. Some results of numerical simulation are provided to verify the stability and feasibility of our method in dealing with the considered problem.
基金The Project Supported by National Natural Science Foundation of China(10071045)
文摘A class of nonlinear for singularly perturbed problems for reaction diffusion equations with time delays are considered. Under suitable conditions, using theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems are studied.
基金The Importent Study Profect of the National Natural Science Poundation of China(90211004)The Natural Sciences Foundation of Zheiiang(102009)
文摘A class of nonlinear singularly perturbed problems for reaction diffusion equations are considered. Under suitable conditions, by using the theory of differential inequalities, the asymptotic behavior of solutions for the initial boundary value problems are studied, reduced problems of which possess two intersecting solutions.
基金Supported by the National Natural Sciences Foundation of China(40676016 and 10471039)the National Key Project for Basic Research(2003CB415101-03 and 2004CB418304)+2 种基金the Key Project of the Chinese Academy of Sciences(KZCX3-SW-221)in part by E-Institutes of Shanghai Municipal Education Commission(N.E03004)the Natural Science Foundation of Zeijiang,China(Y606268).
文摘In this article the travelling wave solution for a class of nonlinear reaction diffusion problems are considered. Using the homotopic method and the theory of travelling wave transform, the approximate solution for the corresponding problem is obtained.
基金Project supported by the National Natural Science Foundation of China （Nos. 40676016, 10471039）, the National Key Basic Research Special Foundation of China （No. 2004CB418304）, the Key Basic Research Foundation of the Chinese Academy of Sciences （No. KZCX3-SW-221） and in part by EInstitutes of Shanghai Municipal Education Commission （No. E03004）
文摘In this paper, a class of nonlinear singularly perturbed initial boundary value problems for reaction diffusion equations with boundary perturbation are considered under suitable conditions. Firstly, by dint of the regular perturbation method, the outer solution of the original problem is obtained. Secondly, by using the stretched variable and the expansion theory of power series the initial layer of the solution is constructed. And then, by using the theory of differential inequalities, the asymptotic behavior of the solution for the initial boundary value problems is studied. Finally, using some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.
基金the National Natural Science Foundation of China (Nos.40676016 and 40876010)the National Basic Research Program (973) of China (Nos.2003CB415101-03 and 2004CB418304)+2 种基金the Knowledge Innovation Project of Chinese Academy of Sciences (No.KZCX2-YW-Q03-08)LASG State Key Laboratory Special FundE-Institutes of Shanghai Municipal Education Commission (No.E03004)
文摘A class of differential-difference reaction diffusion equations with a small time delay is considered.Under suitable conditions and by using the method of the stretched variable,the formal asymptotic solution is constructed.And then,by using the theory of differential inequalities the uniformly validity of solution is proved.
基金Supported by the National Natural Science Foundation of China (90111011 and 10471039)the National Key Project for Basics Research (2003CB415101-03 and 2004CB418304)the Key Project of the Chinese Academy of Sciences (KZCX3-SW-221)the Natural Science Foundation of Zhejiang (Y604127).
文摘The nonlinear nonlocal singularly perturbed initial boundary value problems for reaction diffusion equations with a boundary perturbation is considered. Under suitable conditions, the outer solution of the original problem is obtained. Using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed. And then using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems is studied. Finally the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.
基金Supported by the National Natural Science Foundation of China(11202106)the Natural Science Foundation of the Education Department of Anhui Province(KJ2014A151)the Natural Sciences Foundation from the Universities of Jiangsu Province(13KJB170016)
文摘The singular perturbation problem for reaction diffusion time delay equation with boundary perturbation is considered. Firstly, the outer solution for the initial boundary value problem is constructed. Then, the initial and boundary layer correction terms are obtained using the stretched variables transforms. Finally, the asymptotic behavior of solution for the initial boundary value problem is studied.
基金Supported by the National Natural Science Foundation of China(11371248)the Natural Science Foundation of the Education Department of Anhui Province 3(KJ2013A133,KJ2013B003)the Natural Science Foundation of Zhejiang Province(LY13A010005)
文摘A class of singularly perturbed Robin problems for reaction diffusion equation is considered. Under suitable conditions the asymptotic behavior of the generalized solution for the problems are studied.
基金Supported by the National Natural Science Foundation of China (40676016 and 10471039)the National Key Basic Research Special Foundation of China (2004CB418304)+1 种基金the Key Basic Research Foundation of the Chinese Academy of Sciences (KZCX3-SW-221)in part by E-Institutes of Shanghai Municipal Education Commission (N.E03004).
文摘A class of nonlinear initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions and using the theory of differential inequalities the asymptotic solution of the initial boundary value problems is studied.
文摘This paper studies the time asymptotic behavior of solutions for a nonlinear convection diffusion reaction equation in one dimension.First,the pointwise estimates of solutions are obtained,furthermore,we obtain the optimal Lp,1≤ p ≤ ＋∞,convergence rate of solutions for small initial data.Then we establish the local existence of solutions,the blow up criterion and the sufficient condition to ensure the nonnegativity of solutions for large initial data.Our approach is based on the detailed analysis of the Green function of the linearized equation and some energy estimates.
基金Supported by the National Natural Scince Foundation of China( 1 0 0 71 0 4 8) ,and the"Hundred TalentsProject"of Chinese Academy of Sciences
文摘The singularly perturbed initial boundary value problems for reaction diffusion equations are considered.Under suitable conditions and by using the theory of differential inequality,the asymptotic behavior of solution for initial boundary value problems are studied,where the reduced problems possess two intersecting solutions.
文摘A mathematical model of CE reaction schemes under first or pseudo-first order conditions with different diffusion coefficients at a spherical electrode under non-steady-state conditions is described. The model is based on non-stationary diffusion equation containing a non-linear reaction term. This paper presents the complex numerical method (Homotopy perturbation method) to solve the system of non-linear differential equation that describes the homogeneous processes coupled to electrode reaction. In this paper the approximate analytical expressions of the non-steady-state concentrations and current at spherical electrodes for homogeneous reactions mechanisms are derived for all values of the reaction diffusion parameters. These approximate results are compared with the available analytical results and are found to be in good agreement.
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.
基金The project is supported by the National Natural Science Foundation of China(No.10071048)
文摘The singularly perturbed initial boundary value problem for a class of reaction diffusion equation is considered. Under appropriate conditions, the existence-uniqueness and the asymptotic behavior of the solution are showed by using the fixed-point theorem.
基金Project supported by the National Natural Science Foundation of China (No. 40876010)the Major Projects of Knowledge Innovation Program of Chinese Academy of Sciences (No. KZCX2-YW-Q03-08)+2 种基金the Research and Development Special Fund for Public Welfare Industry (No. GYHY200806010)the Special Fund of the State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, the Foundation of Shanghai Municipal Education Commission(No. E03004)the Natural Science Foundation of Zhejiang Province (No. Y6090164)
文摘A class of initial boundary value problems of differential-difference equations for reaction diffusion with a small time delay is considered. Under suitable conditions and by using the stretched variable method, a formal asymptotic solution is constructed. Then, by use of the theory of differential inequalities, the uniform validity of the solution is proved.
基金Project supported by the National Natural Science Foundation of China (Nos. 90111011 and 10471039) the E-Institute of Shanghai Municipal Education Commission (N. E03004) the Natural Science Foundation of Zhejiang Province (Y604127)
文摘A class of nonlinear nonlocal for singularly perturbed Robin initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions, first, the outer solution of the original problem was obtained. Secondly, using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer was constructed. Finally, using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems was studied, and educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation were discussed.
基金Supported by the Natural Science Foundation of Shaanxi Province(2019JM-534)the Youth Innovation Team of Shaanxi Universities+7 种基金the 14th Five Year Plan for Educational Science in Shaanxi Province(SGH21Y0308)Key Topic of China Higher Education Association(21DFD04)Higher Education Teaching Reform Project of Xi’an International University(2023B03)2022 Annual Planning Project of China Association of Private Education(School Development)(CANFZG22222)Project of Department of Education of Shaanxi Provincethe 2022 Annual Topic of the"14th Five-Year Plan"of Shaanxi Provincial Educational Science(SGH22Y1885)Project of Qi Fang Education Research Institute of Xi’an International University(23mjy10)Special Project of the Shaanxi Provincial Social Science Found in 2023(2023SJ12,2023LS04)。
文摘In this paper,a class of slow reaction-diffusion equations with nonlocal source and inner absorption terms are studied.By using the technique of improved differential inequality,the lower bounds of blow up time for the system under either homogeneous Dirichlet or nonhomogeneous Neumann boundary conditions are obtained.
