4 research outputs found
Two-parameter asymptotic expansions for elliptic equations with small geometric perturbation and high contrast ratio
We consider the asymptotic solutions of an interface problem corresponding to
an elliptic partial differential equation with Dirich- let boundary condition
and transmission condition, subject to the small geometric perturbation and the
high contrast ratio of the conductivity. We consider two types of
perturbations: the first corresponds to a thin layer coating a fixed bounded
domain and the second is the per perturbation of the interface. As the
perturbation size tends to zero and the ratio of the conductivities in two
subdomains tends to zero, the two-parameter asymptotic expansions on the fixed
reference domain are derived to any order after the single parameter expansions
are solved be- forehand. Our main tool is the asymptotic analysis based on the
Taylor expansions for the properly extended solutions on fixed domains. The
Neumann boundary condition and Robin boundary condition arise in two-parameter
expansions, depending on the relation of the geometric perturbation size and
the contrast ratio