On the approximate solvability of a strongly nonlinear transmission problem from macrobiology

Abstract

Constructive existence results for the variational solution of a strongly nonlinear transmission problem are extended to unbounded regions by employing an exhausting sequence of approximating domains. In particular, a nonlocal formulation is obtained on bounded domains through a linearization of the far field exterior to an auxilliary boundary. Using the theory of monotone operators, we demonstrate existence and uniqueness of the weak solution to an electrostatic problem from macrobiology as well as the strong convergence of the Galerkin approximation.

Keywords:

• Dirichlet-Neumann map
• Galerkin approximation
• Debye-Hückel theory
• Poisson-Boltzmann equation