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
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.
