The Neumann problem with a small parameter (Formula presented.) is considered in this paper. The operators L0and L1are self-adjoint second order operators. We assume that L0has a non-negative characteristic form and L1is strictly elliptic. The reflection is with respect to inward co-normal unit vector γε(x). The behavior of limε↓0uε(x) is effectively described via the solution of an ordinary differential equation on a tree. We calculate the differential operators inside the edges of this tree and the gluing condition at the root. Our approach is based on an analysis of the corresponding diffusion processes.
- Averaging principle
- Diffusion processes on a graph
- Equations with non-negative characteristic form
- Second order equations with a small parameter