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
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.
