In this paper, a class of strongly nonlinear singular perturbed boundary value problems are coasidered by the theory of differential inequalities and the correction of boundary layer, under which the existence of solu...In this paper, a class of strongly nonlinear singular perturbed boundary value problems are coasidered by the theory of differential inequalities and the correction of boundary layer, under which the existence of solution is proved and the uniformly valid asymptotic expansions is obtained as well.展开更多
In this paper we consider the stationary multijunction device model with the avalanche effect. Using the singular perturbation method, an approximation to the current voltage curve is obtained. The cause and the condi...In this paper we consider the stationary multijunction device model with the avalanche effect. Using the singular perturbation method, an approximation to the current voltage curve is obtained. The cause and the condition for the occurrence of saturation current is analyzed. Especially, it is pointed that the avalanche effect is responsible for the blowing up of the saturation current. We prove the existence of multiple steady state solution when the ionization rate is relatively small. Finally, some numerical examples are presented to show the reliability of the theoretical results.展开更多
The nonlinear predator-prey singularly perturbed Robin initial boundary value problems for reaction diffusion systems were considered. Under suitable conditions, using theory of differential inequalities the existence...The nonlinear predator-prey singularly perturbed Robin initial boundary value problems for reaction diffusion systems were considered. Under suitable conditions, using theory of differential inequalities the existence and asymptotic behavior of solution for initial boundary value problems were studied.展开更多
A class of singularly perturbed problems for the nonlinear elliptic equations is considered. Under suitable conditions, using the theory of differential inequalities the asymptotic behavior of solution for the boundar...A class of singularly perturbed problems for the nonlinear elliptic equations is considered. Under suitable conditions, using the theory of differential inequalities the asymptotic behavior of solution for the boundary value problems are studied, which reduced equations possess two intersecting solutions.展开更多
A class of nonlocal singnlarly perturbed problems for the hyperbolic dif-ferential equation are considered. Under snitable conditions, we discuss the asymptoticbehavior of solution for the initial boundary value probl...A class of nonlocal singnlarly perturbed problems for the hyperbolic dif-ferential equation are considered. Under snitable conditions, we discuss the asymptoticbehavior of solution for the initial boundary value problems.展开更多
The singularly perturbed problems for the nonlinear elliptic systems in the half space are considered. Under suitable conditions, using the comparison theorem the existence and asymptotic behavior of solution for the ...The singularly perturbed problems for the nonlinear elliptic systems in the half space are considered. Under suitable conditions, using the comparison theorem the existence and asymptotic behavior of solution for the boundary value problem are studied.展开更多
In the present paper, we have investigated the peristaltic flow of hyperbolic tangent fluid in a curved channel. The governing equations of hyperbolic tangent fluid model for curved channel are derived including the e...In the present paper, we have investigated the peristaltic flow of hyperbolic tangent fluid in a curved channel. The governing equations of hyperbolic tangent fluid model for curved channel are derived including the effects of curvature. The highly nonlinear partial differential equations are simplified by using the wave frame transformation,long wave length and low Reynolds number assumptions. The reduced nonlinear partial differential equation is solved analytically with the help of homotopy perturbation method (HPM). The physical features of pertinent parameters have been discussed by plotting the graphs of pressure rise and stream functions.展开更多
In this paper, we have investigated the peristaltic flow of Williamson fluid in a curved channel. The governing equations of Williamson fluid model for curved channel are derived including the effects of curvature. Th...In this paper, we have investigated the peristaltic flow of Williamson fluid in a curved channel. The governing equations of Williamson fluid model for curved channel are derived including the effects of curvature. The highly nonlinear partial differential equa- tions are simplified by using the wave frame transformation, long wavelength and low Reynolds number assumptions. The reduced nonlinear partial differential equation is solved analytically with the help of homotopy perturbation method. The physical features of pertinent parameters have been discussed by plotting the graphs of pressure rise, velocity profile and stream functions.展开更多
基金Foundation item: Supported by Important Study Project of the National Natural Science Foundation of China (No. 90211004) and the Natural Science Foundation of Zhejiang (No. 102009).
基金Supported by the Natural Science Foundation of Zhejiang Provivce (102009)Supported by the Natural Foundation of Huzhou Teacher's College(200302)
文摘In this paper, a class of strongly nonlinear singular perturbed boundary value problems are coasidered by the theory of differential inequalities and the correction of boundary layer, under which the existence of solution is proved and the uniformly valid asymptotic expansions is obtained as well.
文摘In this paper we consider the stationary multijunction device model with the avalanche effect. Using the singular perturbation method, an approximation to the current voltage curve is obtained. The cause and the condition for the occurrence of saturation current is analyzed. Especially, it is pointed that the avalanche effect is responsible for the blowing up of the saturation current. We prove the existence of multiple steady state solution when the ionization rate is relatively small. Finally, some numerical examples are presented to show the reliability of the theoretical results.
基金Important Study Project of the NationalNatural Science F oundation of China( No.90 2 110 0 4),and"Hun-dred Talents Project"of Chinese Academy of Sciences
文摘The nonlinear predator-prey singularly perturbed Robin initial boundary value problems for reaction diffusion systems were considered. Under suitable conditions, using theory of differential inequalities the existence and asymptotic behavior of solution for initial boundary value problems were studied.
文摘A class of singularly perturbed problems for the nonlinear elliptic equations is considered. Under suitable conditions, using the theory of differential inequalities the asymptotic behavior of solution for the boundary value problems are studied, which reduced equations possess two intersecting solutions.
基金The project is supported by the National Natural Science Foundation of China(10071048)
文摘A class of nonlocal singnlarly perturbed problems for the hyperbolic dif-ferential equation are considered. Under snitable conditions, we discuss the asymptoticbehavior of solution for the initial boundary value problems.
文摘The singularly perturbed problems for the nonlinear elliptic systems in the half space are considered. Under suitable conditions, using the comparison theorem the existence and asymptotic behavior of solution for the boundary value problem are studied.
文摘In the present paper, we have investigated the peristaltic flow of hyperbolic tangent fluid in a curved channel. The governing equations of hyperbolic tangent fluid model for curved channel are derived including the effects of curvature. The highly nonlinear partial differential equations are simplified by using the wave frame transformation,long wave length and low Reynolds number assumptions. The reduced nonlinear partial differential equation is solved analytically with the help of homotopy perturbation method (HPM). The physical features of pertinent parameters have been discussed by plotting the graphs of pressure rise and stream functions.
文摘In this paper, we have investigated the peristaltic flow of Williamson fluid in a curved channel. The governing equations of Williamson fluid model for curved channel are derived including the effects of curvature. The highly nonlinear partial differential equa- tions are simplified by using the wave frame transformation, long wavelength and low Reynolds number assumptions. The reduced nonlinear partial differential equation is solved analytically with the help of homotopy perturbation method. The physical features of pertinent parameters have been discussed by plotting the graphs of pressure rise, velocity profile and stream functions.
