The generalized asymptotic solution for nonlinear singular perturbation reaction diffusion problem[J]. Acta Scientiarum Naturalium Universitatis SunYatseni, 2016,55(2):23-27.
The generalized asymptotic solution for nonlinear singular perturbation reaction diffusion problem[J]. Acta Scientiarum Naturalium Universitatis SunYatseni, 2016,55(2):23-27. DOI: 10.13471/j.cnki.acta.snus.2016.02.005.
The nonlinear singular perturbation interior layer initial boundary value problem for the reaction diffusion equation is considered. Under suitable conditions
the reduced problem generalized outer solution is discussed. By introducing a stretched variable
the formal asymptotic expansion for the generalized solution with interior layer and initial layer corrective terms is constructed. Finally
using the fixed point theory of functional analysis
the existence and uniformly valid interior shock asymptotic solution for the original initial boundary value problems are proved.