This paper deals with the initial-bounndary value problem for the wider nonlinear reaction diffusion system: where Leading into the variables of multiple scales, we obtained a uniformly valid asymptotic solution to an...This paper deals with the initial-bounndary value problem for the wider nonlinear reaction diffusion system: where Leading into the variables of multiple scales, we obtained a uniformly valid asymptotic solution to any degree of precision by using comparison theorem.展开更多
A nonlinear reaction diffusion equations for activator inhibitor systems is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained, secondly, using the variables of mult...A nonlinear reaction diffusion equations for activator inhibitor systems is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained, secondly, using the variables of multiple scales and the expanding theory of power series the formal asymptotic expansions of the solution are constructed, and finally, using the theory of differential inequalities the uniform validity and asymptotic behavior of the solution are studied.展开更多
A singularly perturbed combustion reaction diffusion Robin boundary value problem is considered. Using the theory of differential ineaqality, the existence of solution to the problem is proved and the asymptotic esti...A singularly perturbed combustion reaction diffusion Robin boundary value problem is considered. Using the theory of differential ineaqality, the existence of solution to the problem is proved and the asymptotic estimation of the solution is obtained.展开更多
A class of singularly perturbed initial boundary value problems of reaction diffusion equations for the nonlinear boundary condition with two parameters is considered. Under suitable conditions, by using the theory of...A class of singularly perturbed initial boundary value problems of reaction diffusion equations for the nonlinear boundary condition with two parameters is considered. Under suitable conditions, by using the theory of differential inequalities, the existence and the asymptotic behaviour of the solution for the initial boundary value problem are studied. The obtained solution indicates that there are initial and boundary layers and the thickness of the boundary layer is less than the thickness of the initial layer.展开更多
The singularly perturbed nonlinear problem εy" = f(x, y’)y + g(x, y’), 0 <x < 1, 0 < ε << 1, y(0) = A, y(1) = B, where y, f, g, A, B are n-dimensional vectors is considered. Using the iteration...The singularly perturbed nonlinear problem εy" = f(x, y’)y + g(x, y’), 0 <x < 1, 0 < ε << 1, y(0) = A, y(1) = B, where y, f, g, A, B are n-dimensional vectors is considered. Using the iteration method and the theory of differential inequalities, the existence and asymptotic behavior of solution for the boundary value problems are studied.展开更多
A nonlinear singularly perturbed problems for reaction diffusion equationwith boundary perturbation is considered. Under suitable conditions, the asymptotic behavior ofsolution for the initial boundary value problems ...A nonlinear singularly perturbed problems for reaction diffusion equationwith boundary perturbation is considered. Under suitable conditions, the asymptotic behavior ofsolution for the initial boundary value problems of reaction diffusion equations is studied usingthe theory of differential inequalities.展开更多
The nonlocal singularly perturbed problems for the hyperbolic differential equation are considered. Under suitable conditions, using the fixed point theorem, the asymptotic behavior of solution for the initial boundar...The nonlocal singularly perturbed problems for the hyperbolic differential equation are considered. Under suitable conditions, using the fixed point theorem, the asymptotic behavior of solution for the initial boundary value problems is studied.展开更多
The El Nifio-Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific Oceanatmosphere interactions. In this paper, an asymptotic method of solving the nonlinear equation for the ENSO...The El Nifio-Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific Oceanatmosphere interactions. In this paper, an asymptotic method of solving the nonlinear equation for the ENSO model is used. And based on a class of oscillator of ENSO model, the approximate solution of a corresponding problem is studied by employing the perturbation method. Firstly, an ENSO model of nonlinear time delay equation of equatorial Pacific is introduced, Secondly, by using the perturbed method, the zeroth and first order asymptotic perturbed solutions are constructed. Finally, from the comparison of the values for a figure, it is seen that the first asymptotic perturbed solution using the perturbation method has a good accuracy. And it is proved from the results that the perturbation method can be used as an analytic operation for the sea surface temperature anomaly in the equatorial Pacific of the atmosphere-ocean oscillation for the ENSO model.展开更多
A class of nonlinear singularly perturbed problems for reaction diffusion equations with boundary perturbation are considered. Under suitable conditions, the asymptotic behavior of solution for the initial boundary va...A class of nonlinear singularly perturbed problems for reaction diffusion equations with boundary perturbation are considered. Under suitable conditions, the asymptotic behavior of solution for the initial boundary value problems is studied using the theory of differential inequalities.展开更多
A coupled system of the interdecadal sea-air oscillator model is studied. The E1 Nifio-southem oscillation （ENSO） atmospheric physics oscillation is an abnormal phenomenon involved in the tropical Pacific ocean-atmo...A coupled system of the interdecadal sea-air oscillator model is studied. The E1 Nifio-southem oscillation （ENSO） atmospheric physics oscillation is an abnormal phenomenon involved in the tropical Pacific ocean-atmosphere interactions. The oscillator model is involved with the variations of both the eastern and western Pacific anomaly pat- terns. This paper proposes an ENSO atmospheric physics model using a method of the perturbation theory. The aim is to create an asymptotic solving method for the ENSO model. Employing the perturbed method, the asymptotic solution of corresponding problem is obtained, and the asymptotic behaviour of the solution is studied. Thus we can obtain the prognoses of the sea surface temperature anomaly and related physical quantities.展开更多
A class of coupled system for the E1 Nifio-Southern Oscillation （ENSO） mechanism is studied. Using the method of variational iteration for perturbation theory, the asymptotic expansions of the solution for ENSO mode...A class of coupled system for the E1 Nifio-Southern Oscillation （ENSO） mechanism is studied. Using the method of variational iteration for perturbation theory, the asymptotic expansions of the solution for ENSO model are obtained and the asymptotic behaviour of solution for corresponding problem is considered.展开更多
文摘This paper deals with the initial-bounndary value problem for the wider nonlinear reaction diffusion system: where Leading into the variables of multiple scales, we obtained a uniformly valid asymptotic solution to any degree of precision by using comparison theorem.
基金the National Natural Science Foundation of China under Grant Nos.40676016 and 10471039the National Key Project for Basics Research under Grant Nos.2003CB415101-03 and 2004CB418304+1 种基金the Key Project of the Chinese Academy of Sciences under Grant No.KZCX3-SW-221in part by E-Insitutes of Shanghai Municipal Education Commission under Grant No.E03004
文摘A nonlinear reaction diffusion equations for activator inhibitor systems is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained, secondly, using the variables of multiple scales and the expanding theory of power series the formal asymptotic expansions of the solution are constructed, and finally, using the theory of differential inequalities the uniform validity and asymptotic behavior of the solution are studied.
基金the National Natural Science Foundation of China (No.10071045).
文摘A singularly perturbed combustion reaction diffusion Robin boundary value problem is considered. Using the theory of differential ineaqality, the existence of solution to the problem is proved and the asymptotic estimation of the solution is obtained.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 40676016 and 40876010)the Knowledge Innovation Project of Chinese Academy of Sciences (Grant No. KZCX2-YW-Q03-08)+1 种基金the Natiural Science Foundation of Zhejiang Province of China (Grant No. 6090164)in part by E-Institutes of Shanghai Municipal Education Commission (Grant No. E03004)
文摘A class of singularly perturbed initial boundary value problems of reaction diffusion equations for the nonlinear boundary condition with two parameters is considered. Under suitable conditions, by using the theory of differential inequalities, the existence and the asymptotic behaviour of the solution for the initial boundary value problem are studied. The obtained solution indicates that there are initial and boundary layers and the thickness of the boundary layer is less than the thickness of the initial layer.
文摘The singularly perturbed nonlinear problem εy" = f(x, y’)y + g(x, y’), 0 <x < 1, 0 < ε << 1, y(0) = A, y(1) = B, where y, f, g, A, B are n-dimensional vectors is considered. Using the iteration method and the theory of differential inequalities, the existence and asymptotic behavior of solution for the boundary value problems are studied.
基金Supported by the National Natural Science Foundation of China(No.90211004 No. 10471039)the Natural Science Foundation of Zhejiang Province (No.102009).
文摘A nonlinear singularly perturbed problems for reaction diffusion equationwith boundary perturbation is considered. Under suitable conditions, the asymptotic behavior ofsolution for the initial boundary value problems of reaction diffusion equations is studied usingthe theory of differential inequalities.
基金the National Natural Science Foundation of China (No. 10071048>
文摘The nonlocal singularly perturbed problems for the hyperbolic differential equation are considered. Under suitable conditions, using the fixed point theorem, the asymptotic behavior of solution for the initial boundary value problems is studied.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 40676016 and 10471039)the State KeyProgram for Basic Research of China (Grant Nos 2003CB415101-03 and 2004CB418304)+2 种基金the Key Project of the Chinese Academy of Sciences (Grant No KZCX3-SW-221)in partly by E-Institutes of Shanghai Municipal Education Commission (Grant NoN.E03004)the Natural Science Foundation of Zhejiang Province,China (Grant No Y606268)
文摘The El Nifio-Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific Oceanatmosphere interactions. In this paper, an asymptotic method of solving the nonlinear equation for the ENSO model is used. And based on a class of oscillator of ENSO model, the approximate solution of a corresponding problem is studied by employing the perturbation method. Firstly, an ENSO model of nonlinear time delay equation of equatorial Pacific is introduced, Secondly, by using the perturbed method, the zeroth and first order asymptotic perturbed solutions are constructed. Finally, from the comparison of the values for a figure, it is seen that the first asymptotic perturbed solution using the perturbation method has a good accuracy. And it is proved from the results that the perturbation method can be used as an analytic operation for the sea surface temperature anomaly in the equatorial Pacific of the atmosphere-ocean oscillation for the ENSO model.
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A class of nonlinear singularly perturbed problems for reaction diffusion equations with boundary perturbation are considered. Under suitable conditions, the asymptotic behavior of solution for the initial boundary value problems is studied using the theory of differential inequalities.
基金Under the auspices of National Natural Science Foundation of China (No.40876010)Key Direction in Knowledge Innovation Programs of Chinese Academy of Sciences (No. KZCX2-YW-Q03-08)+2 种基金Research and Development Special Fund for Public Welfare Industry (Meteorology) (No. GYHY200806010)LASG State Key Laboratory Special Fund, Foundation of E-Institutes of Shanghai Municipal Education Commission (No.E03004)Natural Science Foundation of Education Department of Fujian Province (No.JA10288)
文摘A coupled system of the interdecadal sea-air oscillator model is studied. The E1 Nifio-southem oscillation （ENSO） atmospheric physics oscillation is an abnormal phenomenon involved in the tropical Pacific ocean-atmosphere interactions. The oscillator model is involved with the variations of both the eastern and western Pacific anomaly pat- terns. This paper proposes an ENSO atmospheric physics model using a method of the perturbation theory. The aim is to create an asymptotic solving method for the ENSO model. Employing the perturbed method, the asymptotic solution of corresponding problem is obtained, and the asymptotic behaviour of the solution is studied. Thus we can obtain the prognoses of the sea surface temperature anomaly and related physical quantities.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 90111011 and 10471039）, the National Key Basic Research Special Foundation of China （Grant Nos 2003CB415101-03 and 2004CB418304）, the Key Basic Research Foundation of the Chinese Academy of Sciences （Grant No KZCX3-SW-221） and in part by E-Institutes of Shanghai Municipal Education Commission （Grant No N.E03004）.
文摘A class of coupled system for the E1 Nifio-Southern Oscillation （ENSO） mechanism is studied. Using the method of variational iteration for perturbation theory, the asymptotic expansions of the solution for ENSO model are obtained and the asymptotic behaviour of solution for corresponding problem is considered.
