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
Bifurcation properties of dynamical systems with two parameters are investigated in this paper. The definition of transition set is proposed, and the approach developed is used to investigate the dynamic characteristi...Bifurcation properties of dynamical systems with two parameters are investigated in this paper. The definition of transition set is proposed, and the approach developed is used to investigate the dynamic characteristic of the nonlin- ear forced Duffing system with nonlinear feedback controller. The whole parametric plane is divided into several persistent regions by the transition set, and then the bifurcation dia- grams in different persistent regions are obtained.展开更多
A class of singularly perturbed boundary value problems of weakly non linear equation for fourth order on the interval [a, b] with two parameters is considered. Under suitable conditions, firstly, the reduced solution...A class of singularly perturbed boundary value problems of weakly non linear equation for fourth order on the interval [a, b] with two parameters is considered. Under suitable conditions, firstly, the reduced solution and formal outer solution are constructed using the expansion method of power series. Secondly, using the transformation of stretched variable, the first boundary layer corrective term near x = a is constructed which possesses exponential attenuation behavior. Then, using the stronger transformation of stretched variable, the second boundary layer corrective term near x = a is constructed, wtfich also possesses exponential attenuation behavior. The thickness of second boundary layer is smaller than the first one and forms a cover layer near x = a. Finally, using the theory of differential inequalities, the existence, uniform validity in the whole interval [a, b] and asymptotic behavior of solution for the original boundary value problem are proved. Satisfying results are obtained.展开更多
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.
基金supported by the National Natural Science Foundation of China(10632040)
文摘Bifurcation properties of dynamical systems with two parameters are investigated in this paper. The definition of transition set is proposed, and the approach developed is used to investigate the dynamic characteristic of the nonlin- ear forced Duffing system with nonlinear feedback controller. The whole parametric plane is divided into several persistent regions by the transition set, and then the bifurcation dia- grams in different persistent regions are obtained.
基金Project supported by the NSFC(No.40676016,No.40876010)The Knowledge Innovation Project of the Chinese Academy of Sciences(No.KZCX2-YW-Q03-08)The LASG Stale Key Laboratory Special Fund and in part by E-Institutes of Shanghai Municipal Education Commission(No.E03004)
基金Project supported by the National Natural Science Foundation of China(Nos.40676016 and 10471039)the National Key Project for Basic Research(Nos.2003CB415101-03 and 2004CB418304)+2 种基金the Key Project of the Chinese Academy of Sciences(No.KZCX3-SW-221)in part by E-Insitutes of Shanghai Municipal Education Commission(No.N.E03004)the Natural Science Foundation of Zhejiang Province of China(No.Y606368).
文摘A class of singularly perturbed boundary value problems of weakly non linear equation for fourth order on the interval [a, b] with two parameters is considered. Under suitable conditions, firstly, the reduced solution and formal outer solution are constructed using the expansion method of power series. Secondly, using the transformation of stretched variable, the first boundary layer corrective term near x = a is constructed which possesses exponential attenuation behavior. Then, using the stronger transformation of stretched variable, the second boundary layer corrective term near x = a is constructed, wtfich also possesses exponential attenuation behavior. The thickness of second boundary layer is smaller than the first one and forms a cover layer near x = a. Finally, using the theory of differential inequalities, the existence, uniform validity in the whole interval [a, b] and asymptotic behavior of solution for the original boundary value problem are proved. Satisfying results are obtained.
