Time-independent reaction–diffusion equation with a discontinuous reactive term

Аннотация

A two-dimensional singularly perturbed elliptic equation referred to in applications as the reaction–diffusion equation is considered. The nonlinearity describing the reaction is assumed to be discontinuous on a certain closed curve. On the basis of the generalized asymptotic comparison principle, the existence of smooth solution is proven and the accuracy of the asymptotic approximation is estimated.