摘要
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 under Grant Nos.40676016 and 10471039
the National Key Project for Basics Research under Grant Nos.2003CB415101-03 and 2004CB418304
the Key Project of the Chinese Academy of Sciences under Grant No.KZCX3-SW-221
in part by E-Insitutes of Shanghai Municipal Education Commission under Grant No.E03004
