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 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
Adsorption is one of the most widely applied techniques for environmental remediation. Its kinetics are of great significance to evaluate the performance of a given adsorbent and gain insight into the underlying mecha...Adsorption is one of the most widely applied techniques for environmental remediation. Its kinetics are of great significance to evaluate the performance of a given adsorbent and gain insight into the underlying mechanisms. There are lots of references available concerning adsorption kinetics, and several mathematic models have been developed to describe adsorption reaction and diffusion processes. However, these models were frequently employed to fit the kinetic data in an unsuitable or improper manner. This is mainly because the boundary conditions of the associated models were, to a considerable extent, ignored for data modeling. Here we reviewed several widely-used adsorption kinetic models and paid more attention to their boundary conditions. We believe that the review is of certain significance and improvement for adsorption kinetic modeling.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 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
The authors analyze the existence of the equilibrium point and global exponential stability for Hopfield reaction-diffusion neural networks with time-varying delays by means of the topological degree theory and gener... The authors analyze the existence of the equilibrium point and global exponential stability for Hopfield reaction-diffusion neural networks with time-varying delays by means of the topological degree theory and generalized Halanay inequality. Since the diffusion phenomena and time delay could not be ignored in neural networks and electric circuits, the model presented here is close to the actual systems, and the sufficient conditions on global exponential stability established in this paper, which are easily verifiable, have a wider adaptive range.展开更多
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supported by the National Natural Science Foundation of China (No. 20504012)the New Century Excellent Talents in University of China (No. NCET-07-0421)
文摘Adsorption is one of the most widely applied techniques for environmental remediation. Its kinetics are of great significance to evaluate the performance of a given adsorbent and gain insight into the underlying mechanisms. There are lots of references available concerning adsorption kinetics, and several mathematic models have been developed to describe adsorption reaction and diffusion processes. However, these models were frequently employed to fit the kinetic data in an unsuitable or improper manner. This is mainly because the boundary conditions of the associated models were, to a considerable extent, ignored for data modeling. Here we reviewed several widely-used adsorption kinetic models and paid more attention to their boundary conditions. We believe that the review is of certain significance and improvement for adsorption kinetic modeling.
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This work was supported by the National Natural Science Foundation of China(Grant Nos.10171072 and 19831030).
文摘 The authors analyze the existence of the equilibrium point and global exponential stability for Hopfield reaction-diffusion neural networks with time-varying delays by means of the topological degree theory and generalized Halanay inequality. Since the diffusion phenomena and time delay could not be ignored in neural networks and electric circuits, the model presented here is close to the actual systems, and the sufficient conditions on global exponential stability established in this paper, which are easily verifiable, have a wider adaptive range.
基金Supported by the National Natural Science Foundation of China(No.40676016)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-Institutes of Shanghai Municipal Education Commission(N.E03004).
